Organic-inorganic hybrid perovskite compounds

ABSTRACT

Photoactive materials comprising organic-inorganic hybrid halide perovskite compounds are provided. Photovoltaic cells and light-emitting devices incorporating the photoactive materials into their light-absorbing and light-emitting layers, respectively, are also provided. The halide perovskites have an amAMX3 perovskite crystal structure, wherein am is an alkyl diamine cation, an aromatic diamine cation, an aromatic azole cation, a cyclic alkyl diamine cation or a hydrazinediium cation; A is a monovalent alkylammonium cation or an alkali metal cation; X is a halide ion or a combination of halide ions; and M is an octahedrally coordinated bivalent metal atom.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims priority to U.S. provisional patentapplication No. 62/527,409 that was filed Jun. 30, 2017, the entirecontents of which are hereby incorporated herein by reference.

REFERENCE TO GOVERNMENT RIGHTS

This invention was made with government support under SC0012541 awardedby the U.S. Department of Energy. The government has certain rights inthe invention.

BACKGROUND

Halide perovskites have the A⁺M²⁺X⁻ ₃ structural formula, where A⁺represent a nonbonding univalent cation, M²⁺ is an octahedrallycoordinated bivalent metal ion, and X⁻ is a monoanionic halide ion. Pb,Sn and Ge can form the genuine perovskite structure, because theyfulfill the coordination and charge balance prerequisites. Sn is anespecially attractive candidate since its perovskite analogues possesssimilar, or even superior, optical and electronic characteristicscompared to Pb, exhibiting narrower optical band gaps and highercharge-carrier mobilities. Lead-free methylammonium tin iodide (MASnI₃)perovskite solar cells and tin iodide (FASnI₃) perovskite solar cellshave been reported. Thus far, the efficiency of Sn-based perovskitesolar cells has been low, and the stability of Sn-based perovskite solarcells is usually very poor in air. The low photovoltaic performance andpoor environmental stability of the solar cells comes from the low redoxpotential of Sn²⁺, which tends to oxidize to Sn⁴⁺ when exposed to theatmosphere.

SUMMARY

Photoactive materials comprising discrete single crystals oforganic-inorganic hybrid halide perovskite compounds are provided.Electronic devices, including optoelectronic devices, incorporating thephotoactive materials into their light-absorbing and light-emittinglayers, respectively, are also provided. The devices includephotovoltaic cells; radiation detectors; light-emitting devices, such aslight-emitting diodes; and transistors, including phototransistors.

The halide perovskites have an amAMX₃ crystal structure, where am is analkyl diamine cation (for example, an alkyl diammonium cation), anaromatic diamine cation, an aromatic azole cation, or a cyclic alkyldiamine cation. A is a monovalent alkylammonium cation or an alkalimetal cation (Group I cation), X is a halide ion, and M is anoctahedrally coordinated bivalent metal atom. The diamines can beprimary, secondary, or tertiary diamines. Am can also represent ahydrazinediium cation. In some embodiments, am is an alkylamine-functionalized aromatic azole, such as a histamine. In someembodiments, the am cation is an alkylene diammonium cation. In someembodiments, am is ethylene diammonium, en. In these embodiments, thehalide perovskites can be represented by the formula enAMX₃, wherein enis the ethylene diammonium cation ([NH₃CH₂CH₂NH₃]).

One embodiment of an electronic device comprises: (a) a firstelectrically conductive contact (for example, a first electrode); (b) asecond electrically conductive contact (for example, a secondelectrode); (c) a photoactive material in electrical communication withthe first and second electrically conductive contacts, the photoactivematerial comprising a halide perovskite as described herein. Theelectrically conductive contacts can be configured to pass a currentthrough the photoactive material and/or to apply an electric fieldacross the photoactive material. The optoelectronic devices includedevices, such as photovoltaic cells and radiation detectors, thatconvert incident radiation (photons) into an electrical current orsignal. The radiation detectors can further include a detectorconfigured to detect a photocurrent generated in the photoactivematerial as the result of the absorption of the incident radiation. Theoptoelectronic devices also include devices that convert electricalenergy into light energy, as in the case of a light-emitting diode. In atransistor, the first and second electrically conductive contacts canprovide a source electrode and a drain electrode, respectively.

One embodiment of a photovoltaic cell comprises: (a) a first electrodecomprising an electrically conductive material; (b) a second electrodecomprising an electrically conductive material; (c) a photoactivematerial disposed between (including partially between), and inelectrical communication with, the first and second electrodes, thephotoactive material comprising a halide perovskite as described herein;and (d) a hole transporting material disposed between the first andsecond electrodes and configured to facilitate the transport of holesgenerated in the photoactive material to one of the first and secondelectrodes.

Other principal features and advantages of the invention will becomeapparent to those skilled in the art upon review of the followingdrawings, the detailed description, and the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

Illustrative embodiments of the invention will hereafter be describedwith reference to the accompanying drawings, wherein like numeralsdenote like elements.

FIG. 1A shows the unit cell and crystal structure of an {en}FASnI₃perovskite absorber. FIG. 1B shows pXRD patterns for various {en}FASnI₃perovskites. FIG. 1C shows ¹H Nuclear Magnetic Resonance (NMR) spectrafor {en}FASnI₃ perovskite crystals with various molar ratios of FA anden. FIG. 1D shows thermogravimetric analysis (TGA) spectra for{en}FASnI₃ perovskite crystals with various molar ratios of FA and en.FIG. 1E shows optical absorbance spectra for {en}FASnI₃ perovskitecrystals with various molar ratios of FA and en. FIG. 1F shows thephotoluminescence (PL) spectra for {en}FASnI₃ perovskite crystals withvarious molar ratios of FA and en. FIG. 1G shows a 2×2×2 supercell ofFASnI₃, depicting a model of the hollow perovskite with SnI₂ vacancies(FA₈Sn₅I₁₈). The calculated band structure of the supercell for the full(FA₈Sn₇I₂₂) and hollow (FA₈Sn₅I₁₈) perovskites is shown in panels inFIGS. 1H and 1I, respectively. FIG. 1I inset) depicts a plot of theincrease in the band gap and decrease of the band width as a function ofSnI₂ vacancies in FASnI₃.

FIG. 2A shows a top view Scanning Electron Microscope (SEM) image of theperovskite films without en loading deposited on the mesoporous TiO₂ atlow magnification. FIG. 2B shows a top view SEM image of the perovskitefilms with 10% en loading deposited on the mesoporous TiO₂ at lowmagnification. The insets show top view SEM images of the same films athigh magnifications. FIG. 2C shows X-Ray Diffraction (XRD) patterns ofthe perovskite films with various amounts of en loading deposited onmesoporous TiO₂. FIG. 2D shows UV-vis absorption of the perovskite filmswith various amounts of en loading deposited on mesoporous TiO₂. FIG. 2Eshows PL spectra of the perovskite films with various amounts of enloading deposited on mesoporous TiO₂. FIG. 2F shows Time-ResolvedPhotoluminescence (TRPL) kinetics of the perovskite films with variousamounts of en loading deposited on mesoporous TiO₂.

FIG. 3A is a cross-sectional SEM image of a completed device. FIG. 3Bshows J-V curves of solar cells using a perovskite absorber with variousamounts of en added. FIG. 3C depicts the aging test on theunencapsulated solar cells without and with 10% en under constant AM1.5Gillumination in ambient air.

FIG. 4A shows J-V curves of the best-performing solar cell in Example 1using an {en}FASnI₃ perovskite absorber with 10% en loading measuredunder reverse and forward voltage scans. FIG. 4B shows EQE andintegrated J_(sc) measured from a solar cell with 10% en. FIG. 4C showshistograms of PCEs for 60 solar cells with 10% en. FIG. 4D depicts theefficiency of an encapsulated device with 10% en as a function of thestorage time.

FIG. 5A depicts examples of diamine and histamine cations. FIG. 5B showsexamples of aromatic diamine and aromatic azole cations.

FIGS. 6A-6E depict top view SEM images of an {en}FASnI₃ perovskitecrystals prepared by the mixed cations of FA and en with different molarratios of 1:0 (FIG. 6A); 1:0.1 (FIG. 6B); 1:0.25 (FIG. 6C); 1:0.5 (FIG.6D), and 1:1 (FIG. 6E).

FIG. 7A depicts a top view SEM image of an {en}FASnI₃ perovskite filmprepared by the FASnI₃ precursors with 7.5% en loading grown onmesoporous TiO₂. FIG. 7B shows a top view SEM image of an {en}FASnI₃perovskite film prepared by the FASnI₃ precursors with 10% en loadinggrown on mesoporous TiO₂. FIG. 7C depicts a top view SEM image of an{en}FASnI₃ perovskite film prepared by the FASnI₃ precursors with 12.5%en loading grown on mesoporous TiO₂. FIG. 7D depicts a top view SEMimage of the {en}FASnI₃ perovskite film prepared by the FASnI₃precursors with 15% en loading grown on mesoporous TiO₂.

FIG. 8 depicts the steady-state efficiency of an {en}FASnI₃ solar cellwith 10% en loading at a constant bias voltage of 0.333 V.

FIG. 9A depicts the J-V curve of an {en}FASnI₃ solar cell with an activearea of 0.39 cm² using perovskite absorbers with 10% en loading measuredunder a reverse voltage scan. FIG. 9B depicts the J-V curve of an{en}FASnI₃ solar cell with an active area of 1.1 cm² using perovskiteabsorbers with 10% en loading measured under reverse voltage scan.

FIG. 10 depicts UV-VIS absorption spectra of en/MASnI₃ materials.

FIG. 11 depicts the photoluminescence spectra of all examined materialsfrom Example 1.

FIG. 12 shows UV-VIS absorption spectra of all materials from Example 1along with the pure compound en/FAPbI₃.

FIG. 13 depicts photoluminescence spectra of the examined materials fromExample 1.

FIG. 14 shows UV-VIS absorption spectra of all materials from Example 1along with the pure compound en/MAPbI₃.

FIG. 15 depicts photoluminescence spectra of the examined materials fromExample 1.

FIG. 16A shows representative SEM images of compounds(MA)_(1−x/2)(en)_(x/2)(Pb)_(1−x/2)(I)_(3−x/2), x=0, 0.29, 0.35 and 0.44.FIG. 16B is a schematic representation of the perovskite growth inrhombic dodecahedral and octahedral geometries. Relative to theidealized cubic perovskite, in rhombic dodecahedra the face diagonal ofthe perovskite (110 facets) was exposed, whereas the incorporation of eninduced the perovskite growth from the body diagonal to expose the (111)facets in the octahedral morphology.

FIGS. 17A and 17B show views of the 3D structures of the lead iodideperovskites highlighting their phase transformations. FIG. 17A shows xvalues higher than 0.10 of en into MAPbI₃ at room temperature (RT) ledto a P (left) to a (right) phase transformation. FIG. 17B shows x valuesof 0.39 of en into FAPbI₃ at RT, leading to an α (left) to β (right)phase transformation.

FIG. 18A shows the correlation of the percentage of en in(MA)_(1−x/2)(en)_(x/2)(Pb)_(1−x/2)(I)_(3−x/2) samples towards themeasured crystal density. FIG. 18B shows the correlation of thepercentage of en in (MA)_(1−x/2)(en)_(x/2)(Sn)_(1−x/2)(I)_(3−x/2)samples towards the measured crystal density. There were 15% and 11%decreases in the crystal densities of the most hollow materials, incomparison to the pristine one, respectively (error bars are inside thesquares).

FIG. 19 is a schematic illustration of the structure of the 3D pristineMAPbI₃ perovskite and its transformation from a dense proper perovskitestructure to a hollow 3D structure with increasing amounts of en. Cubes:[PbI₆] octahedra, Spheres: MA cations, Rectangles: ethylenediammonium(en) cations.

FIG. 20A shows optical absorption spectra of compound(MA)_(1−x/2)(en)_(x/2)(Pb)_(1−x/2)(I)_(3−x/2). FIG. 20B shows opticalabsorption spectra of compound(MA)_(1−x/2)(en)_(x/2)(Sn)_(1−x/2)(I)_(3−x/2). FIG. 20C shows emissionspectra of compound (MA)_(1−x/2)(en)_(x/2)(Pb)_(1−x/2)(I)_(3−x/2) withincreasing amounts of en and correlation of amount of en % towards therecorded absorption (FIG. 20E) and emission spectra (FIG. 20F) for allhollow perovskites. FIG. 20D shows emission spectra of compound(MA)_(1−x/2)(en)_(x/2)(Sn)_(1−x/2)(I)_(3−x/2) with increasing amount ofen and correlation of amount of en % towards the recorded absorption(FIG. 20E) and emission spectra (FIG. 20F) for all hollow perovskites.For comparison purposes, in FIGS. 20E and 20F, all various x values werenormalized from 0 to 40% for all materials.

FIG. 21 shows representative SEM images of pristine perovskite αMASnI₃,hollow (MA)_(0.955)(en)_(0.045)(Sn)_(0.955)(I)_(2.955),(MA)_(0.895)(en)_(0.105)(Sn)_(0.895)(I)_(2.895) and(MA)_(0.8)(en)_(0.2)(Sn)_(0.8)(I)_(2.8).

FIG. 22 shows representative SEM images of pristine perovskite α FAPbI₃,hollow (FA)_(0.945) (en)_(0.055)(Pb)_(0.945)(I)_(2.945),(FA)_(0.895)(en)_(0.105)(Pb)_(0.895)(I)_(2.895), and(FA)_(0.805)(en)_(0.195)(Pb)_(0.805) (I)_(2.805).

FIG. 23 shows a correlation of the percentage of en in(FA)_(1−x/2)(en)_(x/2)(Pb)_(1−x/2)(I)_(3−x/2) samples towards thedetermined crystal density (error bars are inside the squares). Therewas a 12% decrease in the crystal density of the 39% containing enmaterial in comparison to the pristine one.

FIG. 24 shows optical absorption spectra of compounds(FA)_(1−x/2)(en)_(x/2)(Pb)_(1−x/2)(I)_(3−x/2) with increasing amount ofen, up to 39%.

FIG. 25 shows photoluminescence spectra of(FA)_(1−x/2)(en)_(x/2)(Pb)_(1−x/2)(I)_(3−x/2) materials.

FIG. 26A shows the J-V curves for a solar cell having en/CsSnI₃ crystalsas absorber material and for a solar cell having CsSnI₃ as an absorbermaterial. FIG. 26B shows the PCE over time for the solar cells of FIG.26A.

DETAILED DESCRIPTION

Photoactive materials comprising crystals of organic-inorganic hybridhalide perovskite compounds are provided. Electronic devicesincorporating the photoactive materials into their light-absorbing,light-emitting layers; and semiconducting and/or electrically conductingmaterials are also provided. The devices include photovoltaic cells;radiation detectors; light-emitting devices, such as light-emittingdiodes; and transistors, including phototransistors.

The crystals can be formed as a collection of discretesingle-crystals—as opposed to a polycrystalline film composed ofrandomly oriented crystalline grains in a continuous film. For example,the perovskite crystals of the present disclosure can be synthesizedunconnected crystals in a loose powder. Moreover, the crystals of thehalide perovskites can be formed as pure crystals—that is crystals madefrom only a single halide perovskite, rather than a mixture of differentforms of halide perovskites. The single crystals can then be formed intoa film of crystals that has a higher purity than a halide perovskitefilm fabricated from components other than single crystals of thetargeted material.

The halide perovskites have an amAMX₃ perovskite crystal structure,wherein am is an alkyl diamine cation, an aromatic diamine cation, anaromatic azole cation, a cyclic alkyl diamine cation, or ahydrazinediium cation; A is an alkali metal cation, such as a K, Rb, orCs cation, or a monovalent organic cation, such as an alkylammoniumcation; X is a halide ion or a combination of halide ions, and M is anoctahedrally coordinated bivalent metal atom. Examples of monovalentalkylammonium cations include methylammonium (CH₃NH₃+; MA),formamidinium (HC(NH)₂)₂ ⁺; FA), methylformamidinium (H₃CC(NH)₂)₂ ⁺),and guanidinium (C(NH)₂)₃ ⁺). X may be, for example, an iodide, abromide, or a mixed iodide/bromide halide. Embodiments of the halideperovskites include tin halide perovskites and lead halide perovskites,such as amMASnI₃, amFASnI₃, amMAPbI₃, and amFAPbI₃.

It should be understood that, the term perovskite crystal structurerefers to ideal cubic perovskite crystals structures and also todistorted and non-stoichiometric structural variants of the cubicperovskites crystal structure, including orthorhombic structures,tetragonal structures, and defect perovskite structures.

The alkyl group of the alkyl diamines can be a linear chain or abranched chain and can be substituted or unsubstituted. The length ofthe hydrocarbon chain in the alkyl group can be in the range from one tofive carbon atoms and, thus, can be a methyl, ethyl, propyl, butyl, orpentyl group. However, the alkyl group can have more than five carbonatoms.

The aryl group of the aromatic diamines and azoles can be substituted orunsubstituted and can be, for example, monocyclic or bicyclic; thearomatic rings typically containing from six to 14 carbon atoms and,more typically, from six to ten carbon atoms.

The cyclic group of the cyclic alkyl diamines can be substituted orunsubstituted and can be, for example, monocyclic or bicyclic; thecyclic rings typically containing from six to 14 carbon atoms and, moretypically, from six to ten carbon atoms.

Examples of amine cations (am) are shown in FIGS. 5A and 5B. In thecation structures, n represents the number of repeat units in an alkylchain. As indicated in the figure, n can be 0, 1, 2, 3, and 4. However,n can also have a higher value. In some embodiments of the halideperovskites, n is not equal to zero; and in some embodiments, n is atleast 2.

Am cations such as ethylenediamine are capable of increasing the bandgapof the compounds without the need to form solid solutions. In addition,increasing the organic content of the halide perovskites through theincorporation of am cations can increase their air stability and/orimprove their photoelectric properties.

In some such embodiments, am is en. Various perovskites of suchembodiments have the chemical formula(A)_(1−x/2)(en)_(x/2)(M)_(1−x/2)(X)_(3−x/2), where x is in the rangefrom 0.01 to 0.90 and, in some embodiments, in the range from 0.01 to0.45. As discussed in detail in Example 3, these embodiments of theperovskites can be referred to as hollow perovskites because theincorporation of en into the three-dimensional (3D) perovskite structureresults in M and X vacancies and discontinuities in the 3D [MX₃]framework. The bandgaps and optical properties of these perovskites canbe tailored in a controlled and systematic manner through the loading ofthe en cation in the material, where a higher loading lead to a blueshift in the bandgap.

Because the perovskites in the crystals retain their 3D perovskitestructure they are suitable for incorporation into electronic devices.For example, halide perovskites that are direct bandgap semiconductorscan be used in photovoltaic cells as photoactive materials that absorblight, such as sunlight, and generate electron-hole pairs. Photovoltaiccells incorporating the halide perovskite single crystals as aphotoactive material can take on a variety of forms. Generally, however,the cells will comprise a first electrode comprising an electricallyconductive material; a second electrode comprising an electricallyconductive material; a light absorbing layer comprising the halideperovskite compounds disposed between (including partially between) andin electrical communication with the first and second electrodes; a holetransporting material, which may be an organic or inorganic holetransport material, disposed between (including partially between) thefirst and second electrodes and configured to facilitate the transportof holes (that is, to provide preferential transport of holes relativeto electrons) generated in the light absorbing layer to one of the firstor second electrodes; and an electron transporting layer, disposedbetween (including partially between) the first and second electrodesand configured to facilitate the transport of electrons (that is, toprovide preferential transport of electrons relative to holes) generatedin the light absorbing layer to one of the first or second electrodes.In some cells, the light absorbing layer takes the form of a porous film(e.g., a film comprising a collection of semiconducting nanoparticles,such as titanium dioxide nanoparticles) coated with the halideperovskites, wherein the coating infiltrates into the pores of theporous film. Other layers commonly used in thin film photovoltaic cells,such as hole blocking layers and the like, may also be incorporated intothe photovoltaic cells. In some embodiments of the photovoltaic cells, ahole transporting layer is disposed between the first electrode and thelight absorbing layer and an electron transporting layer is disposedbetween the second electrode and the light absorbing layer.

Triarylamine derivatives, such as spiro-MeOTAD(2,2′,7,7′-tetrakis(N,N-di-p-methoxyphenylamine)-9,9-spirobifluorene),and poly(triaryl amine) (PTAA) doped with4-isopropyl-4′-methyldiphenyliodonium tetrakis(pentafluorophenyl)borate(TPFB) are examples of suitable organic hole transport materials for usein the present photovoltaic cells.

Various materials may be used as an electron transporting layer,provided the material is capable of transporting electrons generated bythe halide perovskites. Metal oxides, metal sulfides, and organicsemiconductors are suitable materials. Illustrative metal oxides includeTiO₂, ZnO, SnO₂, Nb₂O₅ and SrTiO₃. Illustrative metal sulfides includeZnS and CdS. The metal oxides and sulfides may be doped. Illustrativeorganic semiconductors are n-type polymers, small molecules, andderivatives of small molecules. C60, C70, [6,6]-phenyl-C61-butyric acidmethyl ester (PCBM), indene-C60 bisadduct (ICBA), indene C60 tris adduct(ICTA), bis-PCBM, and combinations thereof are some examples of organicelectron transport materials.

At least one of the two electrodes is desirably transparent to theincident radiation (e.g., solar radiation). The transparent nature ofthe electrode can be accomplished by constructing the electrode from atransparent material or by using an electrode that does not completelycover the incident surface of the cell (e.g., a patterned electrode).One example of a transparent electrode comprises a transparentconducting oxide (e.g., fluorine-doped tin oxide (FTO)) coating on atransparent substrate.

The halide perovskite compounds are characterized by broad absorptionspectra that can be tuned by adjusting the ratio of A to am in thehalide perovskites. By way of illustration, some embodiments of films ofthe halide perovskites can absorb and/or emit radiation in theultraviolet, visible, and/or infrared regions of the electromagneticspectrum. For example, some embodiments of the films absorb radiation inthe wavelength range from 300 nm to 1000 nm and/or emitphotoluminescence with a photoluminescence peak in the wavelength rangefrom 300 nm to 1000 nm upon excitation with incident radiation. Theseabsorption and/or emission characteristics can be achieved using halideperovskites having an A to am molar ratio in the range from 1:0.05 to1:1, including molar ratios in the range from 1:0.05 to 1:0.25, forexample.

Photovoltaic cells comprising light-absorbing layers formed from thehalide perovskite compounds can have high power conversion efficiencies.For example, photovoltaic cells having power conversion efficiencies ofat least 4%, at least 5%, and at least 7% (for example, power conversionefficiencies in the range from 4% to 8%), as measured under AM 1.5 Gstandard conditions, are provided. These power conversion efficienciescan be obtained even using very thin light-absorbing layers havingthicknesses of 500 nm or less. Methods for determining the powerconversion efficiency of a photovoltaic cell are provided in theExample.

Photoluminescent light-emitting devices that incorporate the halideperovskites comprise an incident radiation source configured to generateincident radiation; and a light-emitting layer including a halideperovskite, configured such that it is irradiated by incident radiationfrom the incident radiation source when the source is on. In thephotoluminescent light-emitting devices, the incident radiation and thehalide perovskites are characterized in that the halide perovskiteabsorbs the incident radiation, which induces the emissionphotoluminescence. Optional components of the photoluminescentlight-emitting devices include one or more filters configured to blockemitted photoluminescence radiation having an undesired wavelength,while selectively transmitting emitted photoluminescence at otherwavelengths. The source may also optionally include a photoluminescencedetector configured such that photoluminescence from the light-emittinglayer impinges on the detector when the source is in operation.

Throughout this disclosure, the designations amMASnI₃, amFASnI₃,amMAPbI₃, and amFAPbI₃ are synonymous with the designations am/MASnI₃,am/FASnI₃, am/MAPbI₃, and am/FAPbI₃ and with the designations{am}MASnI₃, {am}FASnI₃, {am}MAPbI₃, and {am}FAPbI₃.

Example 1

This Example illustrates that ethylenediamine (en) can serve as an amcation in the 3D FASnI₃ perovskite structure to form crystals of anovel, hybrid 3D perovskite {en}FASnI₃. (A more detailed structuralanalysis of this perovskite is provided in Example 3.)

Conventional wisdom in the art is that the ASnI₃ perovskite structure isstable only with A=MA⁺, FA⁺ and Cs⁺, and the only way to significantlyincrease the band gap is to use solid solutions such asASnI_(3−x)Br_(x). (See, e.g., Hao, F., et al., Lead-free solid-stateorganic-inorganic halide perovskite solar cells. Nat. Photon. 8, 489-494(2014).) Changes in the A cation result only in small changes in theband gap. This example demonstrates that en can serve as a new cationcapable of achieving band gap increases that compare in magnitude tothose of ASnI_(3−x)Br_(x) solid solutions. With support fromfirst-principles theoretical calculations, these experimental studiesindicated that a new band gap tuning mechanism was in effect that wasstrongly linked to en's ability to create massive Schottky defects inthe 3D structure. Inclusion of en also lead to improved thin-filmcoverage and to inhibition of the Sn²⁺/Sn⁴⁺ oxidation process. Thehybrid material displayed dramatically increased photovoltaicperformance and drastically improved environmental stability compared tothe neat FASnI₃ perovskite.

The new {en}FASnI₃ materials were obtained when en was used as anadditive to fabricate FASnI₃-based perovskite solar cells. The obtainedfilms showed very unusual characteristics, such as the retention of the3D crystal structure of FASnI₃ with increasing amounts of en, showingonly a small lattice expansion. In a series of parallel experiments,bulk samples of several {en}FASnI₃ compositions were synthesized inconcentrated hydroiodic acid (HI). The synthesis protocol involvedadding a stoichiometric mixture of FAI and en in a solution of SnI₂ toan aqueous HI/H₃PO₂ solvent mixture and varying the en ratioincrementally. Crystals with different amounts of en consistently showeda 3D-like morphology (FIGS. 6A through 6E).

The crystal structure of {en}FASnI₃ was determined by single-crystalX-ray diffraction (XRD) (FIG. 1A). Similar to FASnI₃, {en}FASnI₃ adopteda pseudocubic, orthorhombic unit cell having the Amm2 polar space group.The observable change caused by en was a small but constant increase inthe normalized unit cell volume from 251.9 Å³ in pristine FASnI₃ to261.1 Å³ in the 1:1 en/FASnI₃ nominal composition, also seen as a peakshift in the powder XRD (pXRD) patterns of the bulk materials (FIG. 1B).Given that en is too large to fit in the perovskite cage, it wasremarkable to see that it nevertheless incorporated into the 3Dstructure. Since the observed unit cell expansion was too small toaccount for the larger size of en compared to FA (the N . . . N distancewas 3.75 Å in the trans configuration of H₃NCH₂CH₂NH₃ ²⁺ in the enI₂salt), this suggests that certain neutral fragments of suitable sizemust be removed from the structure instead. These are defined asSchottky defects; or if charged {SnI}⁺ species are removed in place ofen (2+), as point defects. Single-crystal refinements showed that theoccupancy of the Sn-site was progressively reduced with increasingamounts of en. The presence of en in the structure was confirmed byproton nuclear magnetic resonance (¹H-NMR) (FIG. 1C). Crystals and filmsof {en}FASnI₃ materials could be dissolved in DMSO-d₆, and the ensignals could be accurately quantified against the FA signals. The en/FAratios determined by the NMR measurements are shown in Table 2. Thepresence of en in FASnI₃ is also supported by thermogravimetric data(TGA) (FIG. 1D) showing an increasing mass loss with increasing enincorporation at the ˜300° C. step, which corresponds to a loss of FAIand enI₂ from the thermal decomposition of the perovskite. The loss ofen at a high temperature indicates that, within the perovskite lattice,en existed in its (+2) form rather than its neutral en (0) form, whichhas a boiling point of ˜116° C.

The optical properties of the {en}FASnI₃ materials were intriguing. Bothof the emission spectra, extracted from diffuse reflectance measurementsof the bulk materials (FIG. 1E) and the photoluminescence (PL) emissionspectra obtained from crystals (FIG. 1F), showed a large blue shift ofthe absorption edges/emission maxima with increased en loading. The blueshift trend suggested an opening of the band gap E_(g), from ˜1.3 eV inthe black FASnI₃ perovskite, all the way to E_(g)˜1.9 eV for the 5:1en/FASnI₃ molar ratio, resulting in an obvious color change from blackto red. The observed blue shift in the band gap of a 3D[SnI₃]-perovskite was striking and could not be explained by a simple Acation replacement, where en and FA occupy the cage space in thestructure. Such a dramatic blue shift has been observed only in solidsolutions ASnI_(3−x)Br_(x). (See, e.g., Hao, F., et al., Lead-freesolid-state organic-inorganic halide perovskite solar cells. Nat.Photon. 8, 489-494 (2014).) Therefore, to increase the gap to such alarge extent, while keeping the 3D motif and a full iodide structure,the band widths of the valence and conduction bands had to be narrowed.

In order to account for the dramatic changes of the optical properties,the “hollow perovskite” concept based on the presence of massiveSchottky defects was invoked (FIG. 1G). (See, e.g., Stoumpos, C. C., etal., Halide perovskites: poor man's high-performance semiconductors.Adv. Mater. 28, 5778-5793 (2016).) If entire neutral fragments of SnI₂are missing from the 3D structure, a hollow structure will emerge. Thislocally fragmented perovskite will feature several broken Sn—I bonds ina non-periodic fashion, so the average structure is a pseudocubiclattice. The elimination of neutral fragments leads to a “hollow” 3D[SnI₃]¹⁻ network with the degree of “hollowness” increasing with anincreasing en/FA ratio. The orbital overlap among the remaining Sn/Iatoms is reduced and, as a consequence, the band widths of the valenceand conduction bands in such as hollow structure narrow, therebyproducing the experimentally observed increase in the band gap. Thisexact picture is captured by Density Functional Theory (DFT)calculations for a 2×2×2 supercell where SnI₂ units have been removed(FIGS. 1G through 1I; see Methods for details). DFT calculationsdirectly pointed to the reduction of the band widths upon structuralrelaxation, with the valence band (VB) showing a much larger decreasecompared to the conduction band (CB). The calculated band gaps increasedproportionally with the number of missing SnI₂ units, in agreement withthe experimentally observed trend in the band gaps of {en}FASnI₃ (FIGS.1H and 1I). The decrease of the energy levels of the VB maxima uponextrusion of SnI₂ units had further implications for the stability ofthe perovskite, since the absolute work function was shifted to lowerenergy and, as a result, the tendency of the materials towards oxidationwas diminished. The model of the hollow perovskite was fully supportedby the lower observed mass densities of the {en}FASnI₃ materials asdetermined by gas pycnometry. The mass density decreased with increasingen/FA ratios and, for any given composition, the experimentally measureddensity was consistently smaller than the theoretically predicteddensity, assuming full atom occupancy in the crystal structure (Table1). Based on the above, it can be concluded that {en}FASnI₃ is anentirely new type of 3D perovskite that is very different from theclassical ASnI_(3−x)Br_(x) and APbI_(3−x)Br_(x) systems.

TABLE 1 Comparison of experimental and theoretical crystal densities ofall reported materials, along with standard deviation. Material/DensitySingle-Crystal Single-Crystal (g cm⁻³) Experiment (Full occupancy) (Snrefined) FASnI₃ 3.594(1) 3.604(3) 3.596(3) 1:0.1 3.479(1) 3.587(3)3.565(3)  1:0.25 3.459(1) 3.547(3) 3.497(3) 1:0.5 3.403(1) 3.536(3)3.467(3) 1:1  3.285(1) 3.507(3) 3.386(3)

Having established the fundamental properties of the new perovskites,the casting of thin films began. One of the major problems associatedwith the successful fabrication of Sn-films comes from the difficulty ofpreparing high-quality, high coverage thin films. Many differentapproaches for film deposition have been reported to improve the filmquality, including thermal evaporation, vapor-assisted deposition, andsolvent engineering methods. These methods, which normally involvecomplex processes that limit large-scale fabrication, were not necessaryhere since {en}FASnI₃ forms highly uniform films using a simple one-stepmethod. FIGS. 2A and 2B show scanning electron microscopy (SEM) imagescomparing perovskite films prepared with FASnI₃ (FIG. 2A) and with{en}FASnI₃ (FIG. 2B) using the one-step method. As shown in FIG. 2A, thefilm coverage was poor for the FASnI₃ film, due to its fastcrystallization. In stark contrast, the {en}FASnI₃ film was muchsmoother, with fewer pinholes, after adding 10% en in the precursorsolution (FIG. 2B). The effect was consistent for several {en}FASnI₃perovskite films with variable en loadings (FIGS. 7A through 7D).

The actual composition of {en}FASnI₃ agreed very well with thestoichiometric addition of en to the precursor solution. The overallagreement was established by comparing the optical absorption, the NMRspectra of the films, and the lattice parameters of the unit cells,extracted from the XRD of the films. To quantify the amount of en in theperovskite films, the ¹H-NMR spectra of the perovskite films prepared bythe precursor with 0%, 10%, and 100% en were also measured. It could beestimated that the molar ratio of en and FA in the final film was veryclose to that in the precursor. FIG. 2C shows the XRD patterns of theperovskite films coated on mesoporous TiO₂ without and with en. Thefilms with en exhibited a shift of the Bragg reflections to smaller 2θangles, compared with the neat FASnI₃ film, suggesting an increase inthe unit cell volume. The parameters on the {en}FASnI₃ film were in goodagreement with the XRD results of the bulk materials. Similar to thebulk materials, the absorption spectra of the {en}FASnI₃ films showedthe same marked difference in bandgap. FIG. 2D shows the opticalabsorption spectra of the {en}FASnI₃ perovskite films with 0%, 10%, and25% en loading. The absorption wavelength systematically decreased withincreased en/FA ratio, and the absorption edge became sharper,indicating that the optical absorption coefficient increased. Theestimated band gap of the perovskite absorbers with 0%, 10%, and 25% enwere 1.4 eV, 1.5 eV, and 1.9 eV, respectively.

FIG. 2E shows the PL spectra of the perovskite films of {en}FASnI₃ withvarious amounts of en deposited on mesoporous TiO₂. The neat FASnI₃perovskite film displayed the typical emission peak at about 905 nm. The{en}FASnI₃ perovskite films with 10% and 25% en/FA ratio displayedemission peaks at about 830 nm and 746 nm, respectively. Theblue-shifted emission spectra were consistent with the results obtainedfrom the UV-vis absorption of the films. FIG. 2F shows the time-resolvedPL (TRPL) kinetics of the {en}FASnI₃ perovskite films. The neat FASnI₃perovskite film had an estimated carrier lifetime of 0.19 ns. Incontrast, the carrier lifetimes of the perovskite films with 10% and 25%en loading were 0.46 ns and 0.68 ns, respectively. The longer carrierlifetime indicated a lower recombination rate, due to the better filmquality and lower carrier density.

FIG. 3A shows a cross-sectional SEM image of a completed solar cellemploying a perovskite absorber with 10% en loading. Two layers wereobserved between the Au electrode and the FTO with blocking TiO₂: a 150nm thick capping layer of {en}FASnI₃ with a thinpoly[bis(4-phenyl)(2,4,6-trimethylphenyl)amine] (PTAA) hole transportinglayer; and a 1 m thick mesoporous TiO₂ layer infiltrated with aperovskite absorber. The effect of en on the solar cell performance wasthen investigated. FIG. 3B shows the photocurrent density-voltage (J-V)curves of three representative solar cells using the perovskiteabsorbers with 0%, 10%, and 25% en loading. The neat FASnI₃ perovskitesolar cell achieved a relatively low power conversion efficiency (PCE)of 1.40% with a V_(oc) of 0.15V, a J_(sc) of 23.76 mA cm⁻² and a fillfactor (FF) of 38.24% when measured under a reverse voltage scan (thatis, from V_(oc) to 0 V). This poor performance can be attributed to poorfilm coverage and serious recombination inside the perovskite absorber.However, the solar cell performance was significantly improved when{en}FASnI₃ was used as an absorber. The material with 10% en loadingachieved a high PCE of 6.94% with a V_(oc) of 0.47V, a J_(sc) of 22.29mA cm⁻², and an FF of 66.41% when measured under reverse voltage scan.There was a significant enhancement in V_(oc) and FF, while the J_(sc)of the devices using the perovskite without and with en were comparable.The solar cells using the perovskite absorber with 25% en loadingyielded a PCE of 2.34%, with a high V_(oc) of 0.55V, a J_(sc) of 7.64 mAcm⁻², and an FF of 55.80% under the same measurement conditions. As theen loading increased, the solar cells achieved a higher V_(oc), but theobtained J_(sc) was lower, a trend which probably can be attributed tothe much wider band gap (up to 1.9 eV) and worse carrier transport.Therefore, it was found that the amount of en loading in the {en}FASnI₃is very critical to the device performance. The highest deviceperformance was obtained from the sample with 10% en loading (Table 3).

To evaluate the stability of the {en}FASnI₃ perovskite absorber inmoisture and oxygen, the unencapsulated films (neat and with 10% enloading) were exposed to the ambient atmosphere. The absorption and XRDresults showed that the {en}FASnI₃ perovskite film with 10% en loadinghad a much better environmental stability than the neat FASnI₃ film. Thedurability of the device performance as a function of the time underconstant AM1.5G illumination in air at room temperature was alsoinvestigated (FIG. 3C). The plot shows that the unencapsulated solarcell using the classical FASnI₃ absorber degraded rapidly and after 20min, and the efficiency decreased from 1.28% to 0% (short-circuit).However, the unencapsulated {en}FASnI₃ device with 10% en under the sameconditions retained 50% of its initial efficiency of 6.23%.

FIG. 4A shows the J-V curves of the best-performing solar cell using theperovskite absorber with 10% en, measured under reverse and forwardvoltage scans. This solar cell achieved a PCE of 7.14% with a V_(oc) of0.480 V; a J_(sc) of 22.54 mA cm⁻²; an FF of 65.96% when measured underreverse voltage scan; a PCE of 6.90% with a V_(oc) of 0.475 V, a J_(sc)of 22.54 mA cm⁻²; and an FF of 64.47% when measured under forwardvoltage scan, showing a small hysteresis. FIG. 4B shows the measuredexternal quantum efficiency (EQE) spectrum of the solar cell using theperovskite absorber with 10% en, displaying a high average value in the300-850 nm wavelength range, which is consistent with the absorptionspectrum of the {en}FASnI₃ perovskite with 10% en loading. Theintegrated J_(sc) calculated from the EQE curve was about 22.29 mA cm⁻²,which is very close to the J_(sc) obtained from the J-V measurements.FIG. 4C shows the histograms of PCEs for 60 solar cells with 10% en. Theaverage V_(oc), J_(sc), FF, and PCE were 0.43±0.02 V, 21.90±1.13 mAcm⁻², 63.83±2.16%, and 6.05±0.46%, respectively, showing high averageperformance and good reproducibility of the {en}FASnI₃ perovskite solarcells. To evaluate the stabilized power output of the {en}FASnI₃ device,the photocurrent of a typical device with 10% en at a maximum powervoltage of voltage of 0.333 V was measured, showing a steady-state PCEof 6.65% with a steady-state current density of 19.98 mA cm⁻² (FIG. 8).Since the uniform {en}FASnI₃ film could be obtained by the simpleone-step method, solar cells with a larger active area were alsofabricated. FIGS. 9A and 9B show the solar cells using the {en}FASnI₃absorbers (10% en) with active areas of 0.39 cm² and 1.1 cm² achievedPCEs of 6.09% and 4.30%, respectively. Finally, the long-term stabilityof the {en}FASnI₃ device was checked. FIG. 4D shows that theencapsulated device was very stable and, even after 1000 h, the devicekept an efficiency of ˜6.37%.

Methods Preparation of Materials and Thin Films

The perovskite crystals were grown without and with en according to themethod reported in the literature. (See, e.g., Stoumpos, C. C., et al.,Semiconducting tin and lead iodide perovskites with organic cations:phase transitions, high mobilities, and near-infrared photoluminescentproperties. Inorg. Chem. 52, 9019-9038 (2013).) 3 mmol of SnCl₂.2H₂O(Sigma, 98%) with various amounts of en (0-3 mmol) was dissolved in amixture of 57% w/w aqueous HI solution (5.1 mL) and 50% aqueous H₃PO₂(1.7 mL) by heating to boiling under constant magnetic stirring forabout 5 min, which formed a bright yellow solution. Subsequently, 3 mmolof formamidine acetate salt (sigma, ≥98.0%) was added to the hot yellowsolution, and the stirring continued for 10 min. After that, thesolution was left to cool to room temperature, and the crystals werecollected by suction filtration and dried in a vacuum oven at 125° C.for 12 h. For the red sample with a molar ratio of 1:5, the synthesisprocess was the same, except for the molar concentration (1 mmol ofSnCl₂.2H₂O, 5 mmol of en, and 1 mmol of formamidine acetate salt).

The process of preparing compact and mesoporous TiO₂ layers on FTO hasbeen reported elsewhere. (See, e.g., Cao, D. H., et al., 2D homologousperovskites as light-absorbing materials for solar cell applications. J.Am. Chem. Soc. 137, 7843-7850 (2015).) First, a compact TiO₂ layer wasspin-coated onto an FTO substrate (Tec15, Hartford Glass) from anethanol solution of titanium isopropoxide at 2000 rpm for 30 s, thenannealed in air at 500° C. for 20 min. Subsequently, a mesoporous TiO₂layer composed of 20 nm particles (Dyesol DSL 18NR-T) was spin-coatedonto the compact layer using a diluted solution in anhydrous ethanol(1:3.5 weight ratio) at 500 rpm for 1 min, then annealed in air at 500°C. for 15 min. Finally, the annealed mesoporous TiO₂ film was dippedinto a 0.02M aqueous TiCl₄ solution at 70° C. for 30 min, and thenannealed at 500° C. for 15 min. For the film fabrication, the FASnI₃precursor solution, consisting of 372.5 mg of home-made Sn₁₂, 172 mg ofFAI (Dyesol), and 24 mg of SnF₂ (Sigma, 99%), was dissolved in 723 μL ofN,N-dimethylformamide and 81 μL of dimethyl sulfoxide. The FASnI₃precursors with 7.5%, 10%, 12.5%, 15%, and 25% en (Sigma, 99.5%),respectively, included an extra 4.8 μL, 6.4 μL, 8 μL, 9.6 μL, and 16 μLof en, respectively. The precursors without or with added en werespin-coated onto the mesoporous layers with a spin rate of 1500 rpm for60 s. The substrates were annealed at 70° C. for 5 min and then annealedat 120° C. for 10 min on a hot plate. The solution of hole transportingmaterial, consisting of 32 mg of PTAA (Sigma Aldrich, 99%) and 3.6 mg of4-isopropyl-4′-methyldiphenyliodonium tetrakis(pentafluorophenyl)borate(TPFB) (TCI America) in 1.6 mL of chlorobenzene, was spin-coated ontothe perovskite films at 1500 rpm for 30 s and then annealed at 70° C.for 5 min. All these procedures were performed in a glove box withoxygen and moisture levels of 0 ppm. To complete the device, a 100 nmthick Au electrode was thermally evaporated on top of the holetransporting layer with a metal mask. The active area of the solar cellswas 0.09 cm².

Materials, Film, and Device Characterization

The morphology of the crystals, films, and devices was characterized bya high-resolution field emission SEM (Hitachi SU8030). XRD spectra ofthe perovskite films and crystals without and with en were obtained on aRigaku Miniflex600 pXRD (Cu Ku graphite, λ=1.5406 Å) operating at 40kV/15 mA with a Kβ foil filter. Optical diffuse-reflectance measurementsof the perovskite crystals and UV-vis absorption spectra of the filmswere performed at room temperature using a Shimadzu UV-3600 UV-vis NIRspectrometer operating in the 200-2000 nm region at room temperature.BaSO₄ was used as a non-absorbing reflectance reference. The generatedreflectance-versus-wavelength data were used to estimate the band gap ofthe material by converting reflectance to absorbance data according tothe Kubelka-Munk equation: α/S=(1−R)²/2R, where R is the reflectance anda and S are the absorption and scattering coefficients, respectively. PLspectra were collected on rhombic dodecahedral crystals of {en}FASnI₃using a Horiba LabRam Evolution high-resolution confocal Ramanmicroscope spectrometer (600 g/mm diffraction grating) equipped with adiode CW laser (473 nm, 25 mW) and a Synapse CCD camera. The incidentlaser beam was parallel to the (010) direction of the crystals andfocused at a ˜1 m spot size. Unless stated otherwise, the maximum poweroutput of the laser source was filtered to 1% of the maximum poweroutput. ¹H NMR spectra were recorded on a 600 MHz Bruker, A600spectrometer. All samples were prepared by dissolving a small portion ofthe dried solids (˜10 mg) in 0.6 mL of DMSO-d₆ solution. Single crystalsof appropriate size were selected for XRD experiments. After screening afew diffraction frames to ensure crystal quality, full sphere data werecollected using a STOE IPDS 2 diffractometer withgraphite-monochromatized Mo Kα radiation (λ=0.71073 Å), operating at 50kV and 40 mA under N₂ flow. Integration and numerical absorptioncorrections on the data were performed using the STOE X-AREA programs.Crystal structures were solved by direct methods and refined byfull-matrix least-squares on F² using the Jana2006 program package.(See, e.g., Petříček, V., et al., Crystallographic computing systemJANA2006: general features. Zeitschrift für Kristallographie-CrystallineMaterials 229, 345-352 (2014).) All data were collected at roomtemperature under nitrogen flow. TGA measurements were performed on aNetzsch's Simultaneous Thermal Analysis system. 30 mg of sample wasplaced inside an alumina cap and heated from 30° C. to 500° C. under Heflow with a heating rate of 5° C./min. A Micromeritics AccuPyc II 1340pycnometer was utilized for the density determination of all samples.400 mg of dry sample was loaded into an aluminum cap (1 mL), and thevolume determination was performed based on He displacement. Each samplewas measured 5 times, and the sample volume was recorded along with itsstandard deviation. The average volume of each sample was used for thedensity calculations.

The EQE spectrum was characterized by an Oriel model QE-PV-SI instrumentequipped with an NIST-certified Si diode. J-V curves were characterizedby a Keithley model 2400 instrument under AM1.5G simulated irradiationwith a standard solar simulator (Abet Technologies). The light intensityof the solar simulator was calibrated by an NREL-certifiedmonocrystalline silicon solar cell. Steady-state efficiency calculationswere performed on a CHI electrochemical workstation. TRPL lifetimes weremeasured with a streak camera setup (Hamamatsu C4334 Streakscope). Theinstrument response function was approximately 4% of the sweep window. Acommercial direct diode-pumped 100 kHz amplifier (Spirit 1040-4, SpectraPhysics) produced a fundamental beam of 1040 nm (350 fs, 4.5 W). Thislight was used to pump a non-collinear optical parametric amplifier(Spirit-NOPA, Spectra-Physics), which delivered high repetition ratepulses. The samples were excited with 560 nm, 0.3 nJ pulses.

TABLE 2 Comparison of initial and final FA/en ratio on NMR and densitymeasurements. Nominal NMR Density 0.1 0.035 0.185 0.25 0.095 0.233 0.50.240 0.320 1 0.315 0.500

TABLE 3 Summary of the photovoltaic parameters of the {en}FASnI₃ solarcells with various amounts of en loading. V_(oc) J_(sc) FF PCE [V] [mAcm⁻²] [%] [%] 7.5%  0.29 23.61 57.35 3.94 10% 0.43 23.22 62.65 6.2712.5%  0.47 20.04 62.16 5.86 15% 0.51 17.33 61.20 5.43

Example 2 Synthesis of en/FASnI₃ (en: 0%, 10%, 25%, 50%, 100%)

3 mmol of SnCl₂.2H₂O (Sigma, 98%) with various amounts ofethylenediamine (0-3 mmol) were dissolved in a mixture of 57% w/waqueous HI solution (5.1 mL) and 50% aqueous H₃PO₂ (1.7 mL) by heatingto boiling under constant magnetic stirring for about 5 min, giving riseto a bright yellow solution. Following this, 3 mmol of formamidineacetate (sigma, ≥98.0%) were added to the hot yellow solution undercontinuous stirring. After that, the reaction was left to cool to roomtemperature, and resulted in black crystals being deposited in allcases. The crystals were collected by suction filtration and dried in avacuum oven at 125° C. for 12 h.

Syntheses of en/MASnI₃ (en: 0%, 10%, 20%, 50%, 60%, 80%, 100%)

3 mmol of SnCl₂.2H₂O (Sigma, 98%) were dissolved in a 57% w/w aqueous HIsolution (8 mL) by heating to boiling under constant magnetic stirringfor about 5 minutes, forming a bright yellow solution. Various amountsof ethylenediamine (0-3 mmol) were then added to 50% aqueous H₃PO₂ (1.7mL) at room temperature (RT; ˜23° C.). This solution was added to thehot reaction solution. Following this, 3 mmol of methylaminehydrochloride (sigma, ≥98.0%) were added to the hot yellow solution. Thesolution was left to cool to RT and resulted in black crystals beingdeposited in all cases. The crystals were collected by suctionfiltration and dried in a vacuum oven at 125° C. for 12 h.

Syntheses of en/FAPbI₃ (en: 0%, 10%, 20%, 50%, 70%, 100%)

3 mmol of Pb(CH₃CO₂)₂.3H₂O (Sigma, 99%) were dissolved in a 57% w/waqueous HI solution (8 mL) by heating to boiling under constant magneticstirring for about 5 minutes. Various amounts of ethylenediamine (0-3mmol) were then added to 50% aqueous H₃PO₂ (1.7 mL) at RT. This solutionwas added to the hot reaction solution. Following this, 3 mmol offormamidine acetate (sigma, ≥98.0%) were added to the reaction. Thesolution was left to cool to RT and resulted in black crystals beingdeposited in the case of 0%, 10%, 20%, 50% and 70% ethylenediamine. Inthe case of 100% en (3 mmol), dark red crystals were deposited. Thecrystals were collected by suction filtration and dried in a vacuum ovenat 125° C. for 12 h.

Syntheses of en/MAPbI₃ (en: 0%, 10%, 20%, 50%, 60%, 70% 100%)

3 mmol of Pb(CH₃CO₂)₂.3H₂O (Sigma, 99%) were dissolved in a 57% w/waqueous HI solution (8 mL) by heating to boiling under constant magneticstirring for about 5 minutes. Various amounts of ethylenediamine (0-3mmol) were then added to 50% aqueous H₃PO₂ (1.7 mL) at RT. This solutionwas added to the hot reaction solution. Following this, 3 mmol ofmethylamine hydrochloride (sigma, ≥98.0%) were added to the hotsolution. The solution was left to cool to RT and resulted in blackcrystals being deposited in the case of 0%, 10%, 20% and 50%ethylenediamine. In the case of 60% (1.8 mmol) and 70% en (2.1 mmol),red crystals were deposited; while in the case of 100% en (3 mmol),orange crystals were deposited. The crystals were collected by suctionfiltration and dried in a vacuum oven at 125° C. for 12 h.

Characterization and Properties

Four novel families of 3-D hollow hybrid perovskites were synthesized,namely en/MASnI₃, en/FASnI₃, en/MAPbI₃, and en/FAPbI₃ containing variousamounts of ethylenediamine (en). Incorporation of en in those materialsallowed the fine tuning of their electronic properties, resulted inimproved air and thermal stability, and enabled the assembly of deviceswith improved power conversion efficiencies.

The materials were characterized using single crystal XRD and powderXRD. In the case of en/MASnI₃, en/FASnI₃ and en/FAPbI₃, all materialscontaining various amounts of ethylenediamine were isostructural to theparent pure material containing 0% ethylenediamine, a phase, based onXRD. However, in the case of en/MAPbI₃, with increasing amounts of en itwas also possible to stabilize the α phase at RT. Variable temperatureXRD measurements were also performed. All materials were found to bethermally stable up to 200° C. In the case of some en/MASnI₃ anden/FASnI₃ compounds, improved stability in air was observed.

Following this, UV-VIS spectroscopy measurements were performed in orderto determine the band gap of each compound. With increasing amounts ofen, the band gaps shifted to higher values, up to a 38% increasecompared to the pure materials (see FIGS. 10, 12 and 14). Additionally,photoluminescence measurements validated this result, as a shift in PLpeaks with increasing amounts of en was also observed (see FIGS. 11, 13and 15). Those findings showed that en may be a part of the framework ofthose compounds.

To verify the hypothesis that en was actually part of the framework andwas responsible for those variations in electronic properties of thosecompounds. ¹H-NMR and density measurements were performed. NMRspectroscopy validated the presence of en in those materials. As thenominal concentration of en in a sample increased, the experimentaldetermined amount of en also increased. Furthermore, densitymeasurements revealed that as the amount of en in the samples increased,the crystal density was diminished (see Tables 4, 5 and 6). Thoseresults showed that en was indeed part of the 3-D structure of theperovskites.

Utilization of the compound FASnI₃ with 10% en for the assembly of asolar cell device gave rise to a very high-power conversion efficiencyof 7.14%, compared to the best performing Sn based perovskite solarcells (see Table 3).

A comparison of the refined unit cell dimensions for the en-materialsalong with their calculated band gaps is shown in Tables 7-9.

TABLE 4 Comparison of the initial, nominal ratio of en and theexperimentally determined ratio from ¹H-NMR spectroscopy, along with thedetermined crystal density for all materials. The experimental crystaldensity was determined using a commercially available pycnometer.MASnI₃ + Initial en NMR en crystal en % ratio ratio density 0 3.649 100.1 0.05 3.649 20 0.2 0.09 3.591(1) 50 0.5 0.21 3.536(1) 60 0.60 0.243.505(1) 80 0.80 0.35 3.469(1) 100 1 0.40 3.301(1)

TABLE 5 Comparison of the initial, nominal ratio of en and theexperimentally determined ratio from ¹H-NMR spectroscopy, along with thedetermined crystal density for all materials. The experimental crystaldensity was determined using a commercially available pycnometer.FAPbI₃ + Initial NMR crystal en % ratio ratio density 0 4.101 10 0.10.06 4.024(1) 20 0.2 0.11 4.000(1) 50 0.5 0.21 3.880(1) 70 0.7 0.273.642(1) 100 1 0.35 3.620(1)

TABLE 6 Comparison of the initial, nominal ratio of en and theexperimentally determined ratio from ¹H-NMR spectroscopy, along with thedetermined crystal density for all materials. The experimental crystaldensity was determined using a commercially available pycnometer.MAPbI₃ + Initial NMR crystal en % ratio ratio density 0 4.1590 10 0.10.03 4.121(1) 20 0.2 0.10 4.058(1) 50 0.50 0.29 3.710(1) 60 0.6 0.353.640(1) 70 0.7 0.40 3.624(1) 100 1 0.44 3.550(1)

TABLE 7 Comparison of the refined unit cell dimension of allen-materials along with their calculated band gaps. The increase of theen concentration leads to an increase in the unit cell dimensions andthe observed band gap for all materials. MASnI₃ + Unit cell dimension aBand gap en % (Å) (eV) 0 6.236 1.18 (black) 10 6.234 1.19>> 20 6.2501.34>> 30 6.259 1.34>> 50 6.26 1.35>> 60 6.27 1.41>> 80 6.27 1.44>> 1006.28 1.51>>

TABLE 8 Comparison of the refined unit cell dimension of allen-materials along with their calculated band gaps. An increase in theen concentration leads to an increase in the unit cell dimensions andobserved band gap for all materials. FAPbI₃ + Unit cell dimension a Bandgap en % (Å) (eV) 0 6.354 1.45 (black)   10 6.354 1.45>> 20 6.354 1.47>>30 6.355 1.47>> 50 6.356 1.48>> 70 6.354 1.48>> 100 9.030 1.96 (darkred)

TABLE 9 Comparison of the refined unit cell dimension of allen-materials along with their calculated band gaps. The increase of theen concentration leads to an increase to the unit cell dimension and theobserved band gap for all materials. MAPbI₃ + Unit cell dimension a Bandgap en % (Å) (eV) 0 6.28 1.52 (black)   10 6.28 1.55>> 20 6.29 1.57>> 506.32 1.62>> 60 6.35 1.97 (dark red) 70 6.35   2 (dark red) 100 6.35 2.1(orange) 

Example 3

In this example, methods of making and the structural and physicalcharacteristics of crystals of en-based hollow iodide perovskites arereported. The hollow perovskites were formulated as(A)_(1−x/2)(en)_(x/2)M_(1−x/2)X_(3−x/2), where x is the amount of enincorporated in the perovskite. Three different types of materials aredescribed, based on MASnI₃((MA)_(1−x/2)(en)_(x/2)(Sn)_(1−x/2)(I)_(3−x/2)), MAPbI₃((MA)_(1−x/2)(en)_(x/2)Pb_(1−x/2)I_(3−x/2)), and FAPbI₃((FA)_(1−x/2)(en)_(x/2)(Pb)_(1−x/2)(I)_(3−x/2)). These systems werestudied for various amounts of ethylene diammonium (en) ranging betweenx=0-44%.

Synthesis

All three families of the (A)_(1−x/2)(en)_(x/2)M_(1−x/2)X_(3−x/2)perovskites were synthesized using an HI/H₃PO₂ solvent mixture that canproduce uniform and high-quality single crystals.

During synthesis optimization, the order of the addition of thereactants, as well as their concentration in the reaction media, playeda role in obtaining hollow perovskites. The ratios of the startingmaterials were based on the stoichiometric formula, targeting the AMX₃compositions. The targeted nominal en:A:M ratios were in the range of:(0.1-1): 1:1. The addition of higher amounts of en led to theco-precipitation of light-colored secondary byproducts, identified bysingle-crystal diffraction to be the ethylenediammonium iodide, enI₂,and ethylenediammonium lead iodide, enPbI₄.2H₂O, for the cases of Sn-and Pb-based perovskites, respectively. In the case of enI₂, themolecular structure was 0D and consisted of single I atoms that werecharge balanced by ethylenediammonium cations. In the case ofenPbI₄.2H₂O, the structure consisted of 1D [PbI₄]²⁻ chains that wereseparated and charge balanced by ethylenediammonium cations. Watermolecules were also present in the structure. The maximum amount of enthat was incorporated in the structure was found not to exceed x=0.44,obtained for the (MA)_(0.78)(en)_(0.22)(Pb)_(0.78)(I)_(2.78)composition. Initially, the metal source was dissolved in the boilingsolvent mixture, followed by the addition of en. If the perovskitizer(A-site cation that can stabilize the perovskite structure) was addedbefore en, then the pristine compounds were formed instantly and theaddition of en had no effect on the already formed perovskite crystals.Upon the addition of the perovskitizer (MA or FA) to the hot reactionsolution, black crystals formed immediately, while uniform red or orangecrystals formed upon cooling of the reaction solution. The color of thecrystals, (MA)_(1−x/2)(en)_(x/2)(Pb)_(1−x/2)(I)_(3−x/2), x=0.35-0.44 and(FA)_(1−x/2)(en)_(x/2)(Pb)_(1−x/2)(I)_(3−x/2), x=0.39, depended on theamount of en, and the metal ion. When an amount of en with x≥0.35 wasincorporated into the framework, it triggered a color change from blackto red and orange (Tables 10-12). Note that the color change onlyoccurred in the Pb perovskites, as only in that instance was the bandgap change large enough to cause this effect.

TABLE 10 Comparison of the refined unit cell dimension of(MA)_(1−x/2)(en)_(x/2)(Sn)_(1−x/2)(I)_(3−x/2) materials along with theircalculated band gaps. The increase of the en concentration led to anincrease to the unit cell dimension and the observed band gap for allmaterials. Unit cell MASnI₃ + parameters a, b, c Unit cell Volume Bandgap en % (Å) (Å³) (eV) 0 6.2360(3), 6.2360(3), 242.77(8) 1.21 (blackcr.) 6.2430(7) 5 6.244(1), 6.244(1),  243.5(3) 1.25>> 6.244(2) 96.2509(3), 6.2509(3), 244.18(8) 1.28>> 6.2493(6) 21 6.2605(2),6.2605(2), 245.89(6) 1.35>> 6.2738(5) 24 6.267(1), 6.267(1),  246.7(3)1.42>> 6.282(2) 36 6.2995(3), 6.2995(3), 249.90(6) 1.45>> 6.2972(3) 406.2994(8), 6.2994(8),  250.2(2) 1.51>> 6.305(2)

TABLE 11 Comparison of the refined unit cell dimensions of(FA)_(1−x/2)(en)_(x/2)(Pb)_(1−x/2)(I)_(3−x/2) materials along with theircalculated band gaps. An increase of the en concentration led to anincrease in the unit cell dimension and the observed band gap for allmaterials. Unit cell Unit cell Volume FAPbI₃ + parameters a × b × cNormalized Band gap en % (Å) (Å³) (eV) 0 6.352(1), 6.358(1), 256.4(2)1.44 (black cr.) 6.348(1) 7 6.358(1), 6.355(2), 257.1(3) 1.53>> 6.362(2)11 6.3637(5), 6.3782(7), 257.8(1) 1.57>> 6.3505(7) 21 6.3766(7),6.371(3), 259.4(5) 1.67>> 6.385(3) 27 6.3808(8), 6.386(3), 259.9(4)1.69>> 6.377(3) 29 6.3817(7), 6.3924(7), 260.0(1) 1.71>> 6.3740(7) 399.038(2), 9.038(2),  262(2) 1.94 (dark red)  12.807(5)

TABLE 12 Comparison of the refined unit cell dimension of(MA)_(1−x/2)(en)_(x/2)(Pb)_(1−x/2)(I)_(3−x/2) materials along with theircalculated band gaps. The increase of the en concentration led to anincrease in the unit cell dimensions and the observed band gap for allmaterials. Unit cell Unit cell Volume MAPbI₃ + parameters a × b × cNormalized Band gap en % (Å) (Å³) (ev) 0 8.8617(3), 8.8617(3), 248.3(2) 1.52 (black cr.) 12.6492(5) 3 8.8814(4), 8.8814(4), 249.5(3) 1.56>>12.6558(8) 10 6.306(1), 6.306(1), 250.3(3) 1.65>> 6.296(2) 29 6.314(3),6.314(3), 252.1(9) 1.73>> 6.324(7) 35 6.3472(8), 6.3472(8), 255.2(2)1.85 (dark red) 6.333(2) 40 6.352(1), 6.352(1), 256.8(3) 2 (red) 6.364(2) 44 6.3814(2), 6.3814(2), 260.38(6)  2.1 (orange)  6.3940(5)

In the case of (MA)_(1−x/2)(en)_(x/2)(Sn)_(1−x/2)(I)_(3−x/2), sixanalogs were synthesized with en loading x=0.05, 0.10, 0.21, 0.24, 0.36,0.40. Uniform black crystals of α-MASnI₃ (non-centrosymmetric tetragonalstructure, P4 mm space group, or as a centrosymmetric cubic structure,Pm-3m space group) were obtained in all cases. Six(FA)_(1−x/2)(en)_(x/2)(Pb)_(1−x/2)(I)_(3−x/2) analogues were synthesizedwith en concentrations of x=0.07, 0.11, 0.21, 0.27, 0.29, 0.39.Following the established synthetic methodology for the isolation of theconventional pristine perovskite α-FAPbI₃ (non-centrosymmetricorthorhombic structure, Amm2 space group, or centrosymmetric cubicstructure, Pm-3m space group), yellow crystals of the δ-FAPbI₃perovskitoid phase were initially precipitated, which were subsequentlyconverted to the black α-phase upon further heating at the solvent'sboiling point. (See, e.g., Stoumpos, C. C.; et al., Inorg. Chem. 2013,52, 9019; and Kaltzoglou, A.; et al., Inorg. Chem. 2017, 56, 6302.)Removing the black crystals from the hot solution, using suctionfiltration, and drying them in an oven at 110° C., enabled thestabilization of the pristine black α phase of FAPbI₃ at roomtemperature for more than 1 week, while absence of the heat treatmentstep could lead to swift transformation to the yellow δ-phase in 24hours. Unlike the pristine perovskite FAPbI₃, addition of en in thereaction medium gave rise to stable, uniform, black(FA)_(1−x/2)(en)_(x/2)(Pb)_(1−x/2)(I)_(3−x/2) crystals in up to x=0.29en loading. The presence of en, even in a small amount, such as x=0.07,stabilized the α-phase of FAPbI₃ (i.e.(FA)_(0.965)(en)_(0.035)(Pb)_(0.965)(I)_(2.965)). Interestingly, byincreasing the amount of en to x=0.39, red crystals of the β-phase(non-centrosymmetric tetragonal structure, P4bm space group, or as acentrosymmetric tetragonal structure, P4/mbm, space group) precipitated.Regarding the (MA)_(1−x/2)(en)_(x/2)(Pb)_(1−x/2)(I)_(3−x/2) hollowperovskites, six en loadings were examined, with x=0.03, 0.10, 0.29,0.35, 0.40 and 0.44. At room temperature the stable MAPbI₃ phase was thetetragonal β-phase (tetragonal structure, I4/mcm space group). Thepresence of en dication enabled the stabilization of the α-MAPbI₃ phaseat room temperature (non-centrosymmetric tetragonal structure, P4 mmspace group, or as a centrosymmetric cubic structure, Pm-3m spacegroup). It was observed that en loadings higher than 0.10 gave rise touniform black α-MAPbI₃ crystals. Remarkably, at x=0.35-0.40 en loading,the α-MAPbI₃ phase precipitated as uniform red crystals, while in thecase of x=0.44 en the crystals were orange.

The phase purity of the resulting materials was confirmed by X-raypowder diffraction (PXRD). All(MA)_(1−x/2)(en)_(x/2)(Sn)_(1−x/2)(I)_(3−x/2) perovskites had exactlythe same PXRD pattern and were isostructural to the pristine α-MASnI₃material (x=0). PXRD studies of the(FA)_(1−x/2)(en)_(x/2)(Pb)_(1−x/2)(I)_(3−x/2) compounds verified theiruniform phase and purity. For x values up to 0.29, the hollowperovskites were isostructural to the pristine α-FAPbI₃, whereas atx=0.39 the appearance of additional diffraction peaks at 2θ=22.3° and26.4° were characteristic of the formation of the pure β-FAPbI₃.(MA)_(1−x/2)(en)_(x/2)(Pb)_(1−x/2)(I)_(3−x/2) hollow perovskitescrystallized at the β phase for x=0-0.10, while for x values up to 0.44all materials were isostructural to the pristine α-MAPbI₃. This was madeclear by the disappearance of the diffraction peak at 2θ=23.7°, whichwas characteristic of the β phase MAPbI₃, giving rise to uniformα-MAPbI₃ crystals. Except for the evaluation of phase purity, PXRDmeasurements revealed that there was a gradual expansion in the unitcell volume with increasing amounts of en in the structure. Indexing ofthe PXRD patterns of all materials sheds light on this observation inall cases (Tables 10-12).

The highest amount of en loading found among all of the hollowperovskites was for orange (MA)_(0.78)(en)_(0.22)(Pb)_(0.78)(I)_(2.78).For the Pb-based compounds, x values above 0.35 of en incorporation inthe structure resulted in the formation of red crystals. However, in thecase of Sn hollow perovskites, with x values up to 0.40 in the crystalstructure, there was no deposition of red crystals since the widerbandgap was still ˜1.51 eV. All(MA)_(1−x/2)(en)_(x/2)(Sn)_(1−x/2)(I)_(3−x/2) crystals were black andformed immediately upon the addition of the perovskitizer, while the red(MA)_(1−x/2)(en)_(x/2)(Pb)_(1−x/2)(I)_(3−x/2) and(FA)_(1−x/2)(en)_(x/2)(Pb)_(1−x/2)(I)_(3−x/2) crystals formed after sometime, when the solution was cooler. The remarkable fact in the chemistrypresented above is that the dication of en has not been known tostabilize the 3D perovskite AMAX₃ structure. The compound enPbI₄.2H₂Odoes not have a perovskite structure and the analogous compound enSnI₄has not previously been reported.

The presence of en in the crystal structure and the exact amount of enloading in a given composition was determined by ¹H-NMR spectroscopy, bydissolving the crystals of all the(A)_(1−x/2)(en)_(x/2)M_(1−x/2)X_(3−x/2) materials in a polar solvent anddetermining the cations ratios based on their NMR signatures. Thequantification was based on both the methyl (—CH₃, δ=2.39 ppm) and theammonium (—NH₃ ⁺, δ=7.49 ppm) protons of the methylammonium cationversus the methylene (—CH₂—, δ=3.02 ppm) and ammonium (—NH₃ ⁺, δ=7.77ppm) protons of the ethylenediammonium (en) cations. In methylammonium,the integration of those peaks revealed a ratio of 1:1, since there werethree protons from the methyl group (—CH₃) and three protons from theamine cation (—NH₃ ⁺). In ethylenediammonium, the ratio of the 2 peakswas 4:6, arising from four—CH₂— protons and six ammonium (—NH₃ ⁺)protons, indicating that en was doubly protonated in solution. The samemethodology was used for all samples. The resulting compositions aretabulated in Table 13.

TABLE 13 Comparison of the nominal ratio of en % used in the synthesisand the experimentally determined one (x) from ¹H-NMR spectroscopy forall 18 new materials. nominal en % 10 20 50 60 70 80 100 MASnI₃ actualen % (x) 5 9 21 24 — 36 40 MAPbI₃ actual en % (x) 3 10 29 35 40 — 44FAPbI₃ actual en % (x) 7 11 21 — 27 29 39

Scanning electron microscopy (SEM) imaging revealed that the morphologyof the crystals also changed upon the incorporation of en (FIG. 16A andFIGS. 21 and 22). The pristine full perovskite materials (x=0) exhibitedthe typical rhombic dodecahedral morphology, whereas all en containingcrystals appeared as regular octahedra. The octahedral morphologyobserved here in the hollow perovskites is unprecedented. The octahedralmorphology requires the growth of the perovskite to occur along its bodydiagonal (111) direction in the cubic aristotype, driven by theorganization of the cations residing at the A-site (FIG. 16B). Theinvolvement of the A-site cations in the crystal growth of the hollowperovskites suggests that the solids tended to terminate their surfaceat the en cations, thereby helping to improve the stability of theperovskites towards humidity.

Air Stability

The incorporation of en into the perovskite structure imparted aremarkable improvement in air stability in the tin systems. For example,the (MA)_(0.8)(en)_(0.2)(Sn)_(0.8)(I)_(2.8) composition was stable forat least 9 days at ambient atmosphere. The PXRD pattern of the highlyhollow perovskite after 9 days in air was exactly the same with thefresh as made sample with no traces of crystalline decompositionproducts. However, after 16 days in air, traces of crystallinedecomposition products started to form as small diffraction peaks, whichdo not belong to the α-MASnI₃ crystal structure, appeared at 20 valuesof 12.50, 220, 29° and 42°. For comparison, the compound(MA)_(0.88)(en)_(0.12)(Sn)_(0.88)(I)_(2.88), which incorporatesapproximately half the amount of en in the framework, is stable in airfor ˜1 day only. In this case decomposition products started to appearon the second day, based on the PXRD measurements, whereas the pristineMASnI₃ analogue itself started to decompose after 10 minutes of airexposure. The enhanced air stability was partly also attributed to the“dilution” of the Sn²⁺ ion content and the disconnected nature of theperovskite framework, which presumably slowed down the oxidationkinetics. The markedly improved air stability appeared to be a commonfeature of the hollow perovskites.

In the case of the red (FA)_(0.805)(en)_(0.195)(Pb)_(0.805)(I)_(2.805)crystals, PXRD measurements revealed that the material was stable in airfor 300 days, stabilized at the β phase.

Regarding the orange crystals of(MA)_(0.78)(en)_(0.22)(Pb)_(0.78)(I)_(2.78) compound, PXRD measurementsrevealed that the material was stable in air for less than 330 days, asan additional diffraction peak at 2θ=11.9° and another one, appearing asa “shoulder” at 2θ=20° coming from crystalline decomposition by-productsappeared.

A combination of physical and spectroscopic methods (XRD, gaspycnometry, ¹H-NMR, TGA, SEM/Energy Dispersive X-RAY (EDX)), were usedto study the hollow perovskites and to assign them the general formula(A)_(1−x/2)(en)_(x/2)(M)_(1−x/2)(X)_(3−x/2). These studies revealed thatthe incorporation of en in the 3D perovskite structure leads to massiveM and X vacancies in the 3D [MX₃] framework, thus the term hollow.Certain results of the studies are highlighted below. Additionalinformation about the studies and the experimental and theoreticalprocedures used can be found in Spanopoulos et al., J. Am. Chem. Soc.,2018, 140(17), pp. 5728-5742, the entire disclosure of which isincorporated herein by reference. As the inventors do not intend tolimit the inventions described herein to the perovskites having thespecific formula shown above, it should be noted that the materials mayalso have other chemical formulas, including the formula(A)_(1−x)(en)_(x)(M)_(1−0.7x)(X)_(3−0.4x), wherein x may be, forexample, in the range from 0.01 to 0.90.

The hollow perovskites were found to undergo compositionally-controlledstructural phase transitions based on their MA/en and FA/en ratio, asillustrated in FIGS. 17A and 17B. The en incorporation into theframework stabilized the β-FAPbI₃ at RT (298 K) and the α-MAPbI₃. Thephase transition for MAPbI₃ progressed from the initial tetragonalβ-phase (I4/mcm space group) to the α-phase (non-centrosymmetrictetragonal structure, P4 mm space group, or as centrosymmetric cubicstructure, Pm-3m space group) above an en loading of x=0.10.

Gas pycnometry was used to assess the content of en in the solids andthe “hollowness” of the structure, using He as the gas displacementmedium. These studies found that the density of the (MA) seriesperovskites decreased systematically as a function of (x), starting fromρ=3.640 (1) g cm⁻³ for the pristine full perovskite to ρ=3.255(1) g cm⁻³for the x=0.40 composition, corresponding to an overall 11% decrease(FIG. 18A). The drastic decrease cannot by accounted for by a simplesubstitution of two MA molecules with one en cation since the massdifference in this case is negligible. Therefore, it was evident that endisplaced part of the heavy atoms in the inorganic framework, includingboth Sn²⁺ and I⁻ ions. The same trend was also observed for the Pbanalogs with maximum en loading, reaching a 12% and 15% density decreasefor (FA)_(0.815)(en)_(0.195)(Pb)_(0.815)(I)_(2.815) (FIG. 23) and(MA)_(0.78)(en)_(0.22)(Pb)_(0.78)(I)_(2.78) (FIG. 18B), respectively(Tables 14-16). A perspective of the transformation from a pristinestructure to a hollow structure is shown schematically in FIG. 19.

Based on the above results, the general composition of the materials wasformulated. In order to determine which chemical composition bestdescribed best the experimental results, nine possible chemical formulaethat could potentially arise from the incorporation of en in the hollowperovskites were tested and compared with the combined array ofexperimental results. The theoretical density of each compound,ρ_(calc), was calculated by using the molecular weight of the formulaand the volume of the unit cell that was determined from indexing thepowder XRD patterns. In all cases the charge of en was considered to be(2+), based on the ¹H-NMR spectra, while in one case the possibilitythat the charge was (+1) considered. In order to compare the results ofthe nine compositions and select the most accurate one, an arbitrarycrystal density difference value, that works as a threshold limit wasintroduced. For that purpose, a difference between the calculated andexperimental crystal density (ρ_(calc)−ρ_(exp)) above 0.1 g cm⁻³ was setto be the cut off limit. The formula which had the fewest compoundsbelow this limit and was also consistent with the fact that it is highlyunlikely for an en molecule to replace only M²⁺ ions in the structure,was determine to be the correct composition. Based on this analysis theperovskites were determined to have the compositionA_((1−x/2))en_((x/2))M_((1−x/2))I_((3−x/2)) (i.e.,MA_((1−x/2))en_((x/2))Sn_((1−x/2))I_((3−x/2)),MA_((1−x/2))en_((x/2))Pb_((1−x/2))I_((3−x/2)) andFA_((1−x/2))en_((x/2))Pb_((1−x/2))I_((3−x/2))).

TABLE 14 Comparison of the initial, nominal ratio of en (the amount thatwas used in the synthesis) and the experimental determined one from¹H-NMR spectroscopy (x), along with the determined crystal density forall (MA)_(1−x/2)(en)_(x/2)(Sn)_(1−x/2)(I)_(3−x/2) materials and thetheoretical crystal density if all the nominal amounts of en entered thestructure. The experimental crystal density was determined using acommercially available pycnometer. Theor. crystal Exp. crystal density(g cm⁻³) MASnI₃ + Nominal NMR en density (g cm⁻³) Based on en % enamount (x) Based on (x) nominal amount 0 3.640(1) 3.636 10 0.1 0.053.591(1) 3.552 20 0.2 0.09 3.536(1) 3.469 50 0.5 0.21 3.505(2) 3.228 600.60 0.24 3.469(1) 3.146 80 0.80 0.36 3.301(1) 2.962 100 1 0.40 3.255(1)2.816

TABLE 15 Comparison of the initial, nominal ratio of en (the amount thatwas used in the synthesis) and the experimental determined one from¹H-NMR spectroscopy (x), along with the determined crystal density forall (FA)_(1−x/2)(en)_(x/2)(Pb)_(1−x/2)(I)_(3−x/2) materials and thetheoretical crystal density of all the nominal amounts of en enteredinto the structure. The experimental crystal density was determinedusing a commercially available pycnometer. Theor. crystal Exp. crystaldensity (g cm⁻³) FAPbI₃ + Nominal NMR en density (g cm⁻³) Based onnominal en % en amount (x) Based on (x) amount 0 4.106(2) 4.101 10 0.10.07 4.024(1) 3.989 20 0.2 0.11 4.000(2) 3.876 50 0.5 0.21 3.880(1)3.547 70 0.7 0.27 3.642(2) 3.337 100 1 0.39 3.620(1) 3.010

TABLE 16 Comparison of the initial, nominal ratio of en (the amount thatwas used in the synthesis) and the experimental determined one from¹H-NMR spectroscopy (x), along with the determined crystal density forall (MA)_(1−x/2)(en)_(x/2)(Pb)_(1−x/2)(I)_(3−x/2) materials and thetheoretical crystal density of all the nominal amounts of en enteredinto the structure. The experimental crystal density was determinedusing a commercially available pycnometer. Theor. crystal Exp. crystaldensity (g cm⁻³) MAPbI₃ + Nominal NMR en density (g cm⁻³) Based onnominal en % en amount (x) Based on (x) amount 0 4.151(2) 4.146 10 0.10.03 4.121(3) 4.025 20 0.2 0.1 4.058(2) 3.935 50 0.50 0.29 3.710(1)3.586 60 0.6 0.35 3.640(1) 3.445 70 0.7 0.40 3.624(1) 3.324 100 1 0.443.550(1) 2.988

Optical Absorption and Photoluminescence

Optical absorption spectra for all the hollow perovskites showed thatwith increasing amount of en the band gap shifted to higher energyvalues (FIGS. 20A-20F). At the maximum en loading in the framework a˜40% increase in the energy bandgap was observed. The parameter thatcontrols the optical properties in 3D perovskite compounds was s/porbitals overlapping among the metal and the halide ions. This overlaprelates directly to the M-X-M φ angle. However, the shape and the natureof the A cation(s) can indirectly affect this angle, causing distortionsto the metal octahedra. With a decreasing φ angle, the band gapincreases and this trend is observed also during phase transitions, fromα to γ and δ phases. Especially in the case of MAPbI₃, during its phasetransitions over a wide temperature range (4.2 K to 400 K) the observedblue shift in the bandgap was relatively small (0.08 eV difference).This effect was more pronounced (0.58 eV difference) during thecompositionally induced phase transitions and was attributed to thedisruption of the crystal lattice by en, or possibly to an“emphanisis-like” behavior (strongly amplified by en incorporation)rather than a thermal expansion mechanism of the band gap widening. Asen was incorporated into the structure and M and I atoms were removedfrom the 3D framework, they created discontinuities in the M-X-M-Xbridges as they were replaced by M-X-vacancy-X moieties. Because of thepresence of a large number of these M²⁺ and I⁻ vacancies, the orbitaloverlap among the remaining M/X atoms was reduced and, as a consequence,the widths of the VBM and CBM narrowed, leading to the experimentallyobserved increase in the bandgap.

All eighteen (18) of the hollow perovskite compounds presented in thiswork are direct band semiconductors as it was verified by the sharp bandedge in absorption spectra and DFT calculations.(MA)_(1−x/2)(en)_(x/2)(Sn)_(1−x/2)(I)_(3−x/2) materials exhibited bandgaps ranging from 1.25 eV to 1.51 eV for x values starting from 0.05 to0.40 (FIG. 20B). For the (MA)_(1−x/2)(en)_(x/2)(Pb)_(1−x/2)(I)_(3−x/2)materials, the band gaps increased from 1.56 eV to 2.1 eV for x valuesspanning from 0.03 to 0.44 (FIG. 20A). Similarly, the(FA)_(1−x/2)(en)_(x/2)(Pb)_(1−x/2)(I)_(3−x/2) hollow perovskitesrevealed bang gaps in the range of 1.53 eV to 1.94 eV for x values from0.07 to 0.39 (FIG. 24). This corresponds to a significant increase of˜20%, ˜40% and ˜35% in the band gap energy, respectively. The band gaptrend was reflected in the crystal color change from black to red andorange observed for the Pb-based hollow perovskites. The band gapincrease can be attributed to the “hollowing out” of the perovskiteframework, which is a form of aperiodic dimensional reduction of thecrystal lattice.

The hollow perovskites exhibited photoluminescence (PL) at roomtemperature that was blue shifted with increasing fractions of en (FIGS.20C and 20D). Photoluminescence is an important property forphotovoltaic applications, as an optimum light absorbing candidateshould not only absorb light efficiently but also emit light in the samemanner. Interestingly, the red and orange crystals of compounds(MA)_(1−x/2)(en)_(x/2)(Pb)_(1−x/2)(I)_(3−x/2) and(FA)_(1−x/2)(en)_(x/2)(Pb)_(1−x/2)(I)_(3−x/2) exhibited no PL. All theSn-based analogues exhibited strong PL emission that covered a rangefrom 991 nm for the pristine MASnI₃ to 718 nm for the(MA)_(0.8)(en)_(0.2)(Sn)_(0.8)(I)_(2.8) (FIG. 20D). The PL emission peakof the pristine compound (no en) was centered at 1.25 eV, matching theband gap energy (1.21 eV) from the absorption spectrum. With increasingfractions of en, the two values started to diverge significantly,reaching a maximum absorption/emission energy difference of 0.22 eV forthe (MA)_(0.8)(en)_(0.2)(Sn)_(0.8)(I)_(2.8) composition, revealing anabove band gap photoluminescence (Table 17). Taking into account thatthis material contains the highest amount of en among all hollowperovskites, it is likely that, due to the existence of a large numberof defects, there could be some spatially confined domains in thestructure that caused lattice strain and gave rise to stable excitonicstates. Those states may have contributed to the increase of the energyof the emission spectrum.

The Pb-based analogs exhibited a similar blue shift with increasingamounts of en, accompanied by an analogous divergence between theabsorption/emission energy. The PL peak maxima of the(FA)_(1−x/2)(en)_(x/2)(Pb)_(1−x/2)(I)_(3−x/2) perovskites ranged between799 nm for the pristine α-FAPbI₃ to 678 nm for the(FA)_(0.855)(en)_(0.145)(Pb)_(0.855)(I)_(2.855) (FIG. 25). Likewise, thePL peaks of the (MA)_(1−x/2)(en)_(x/2)(Pb)_(1−x/2)(I)_(3−x/2) compoundsranged between 766 nm for the pristine β-MAPbI₃ to 644 nm for(MA)_(0.825)(en)_(0.175)(Pb)_(0.825)(I)_(2.825) (FIG. 20C). In bothcases, all Pb based materials exhibited an above band gap PL, with amaximum energy difference of 0.12 eV and 0.13 eV for(FA)_(0.855)(en)_(0.145)(Pb)_(0.855)(I)_(2.855) and(MA)_(0.855)(en)_(0.145)(Pb)_(0.855)(I)_(2.855), respectively,significantly smaller than that observed for the Sn-based hollowperovskite (0.22 eV), which contained much higher amounts of en (Table17).

The unusual feature of the PL in hollow perovskites is that withincreasing en loading, the intensity gradually diminishes and vanishes(at room temperature) for the materials with x>0.35 (FIGS. 20C and 20F).All (FA)_(0.805)(en)_(0.195)(Pb)_(0.805)(I)_(2.805),(MA)_(0.8)(en)_(0.2)(Pb)_(0.8)(I)_(2.8) and(MA)_(0.78)(en)_(0.22)(Pb)_(0.78)(I)_(2.78) compositions exhibited nolight emission. This could be attributed to the special crystal growthof the hollow perovskites (along (111) direction, see above), whichexposed specifically the A-site cations at the crystal edges. Thepresence of significant amounts of en in the crystal surface led to aneffective disconnection of the perovskite structure, which may beresponsible for the loss of PL emission when the local concentration ofen at the surface exceeds a certain limit. Because of the disorder inthe structure, the presence of charged point defects that may act asnonradiative recombination centers (traps) cannot be ruled out.Furthermore, this PL emission absence could be attributed to phononquenching by the large number of vacancies.

TABLE 17 Measured band gap energy (eV) from the absorption spectra andthe corresponding PL peak positions (eV) for all hollow and pristineexamined materials (x = 0). The maximum recorded energy differencevalues were 0.22 eV for the(MA)_(1−x/2)(en)_(x/2)(Sn)_(1−x/2)(I)_(3−x/2) compounds, 0.12 eV for the(FA)_(1−x/2)(en)_(x/2)(Pb)_(1−x/2)(I)_(3−x/2) compounds and 0.13 eV forthe (MA)_(1−x/2)(en)_(x/2)(Pb)_(1−x/2)(I)_(3−x/2) compounds. normalized(MA)_(1−x/2)(en)_(x/2)(Sn)_(1−x/2)(I)_(3−x/2)(FA)_(1−x/2)(en)_(x/2)(Pb)_(1−x/2)(I)_(3−x/2)(MA)_(1−x/2)(en)_(x/2)(Pb)_(1−x/2)(I)_(3−x/2) x % en value Band gap (eV)PL peak (eV) Band gap (eV) PL peak (eV) Band gap (eV) PL peak (eV) 01.21 1.25 1.44 1.55 1.52 1.62 4 1.25 1.27 1.53 1.6 1.56 1.68 10 1.281.31 1.57 1.65 1.65 1.71 20 1.35 1.49 1.67 1.73 1.73 1.86 28 1.42 1.591.69 1.81 1.85 1.93 36 1.45 1.67 1.71 1.83 2 — 40 1.51 1.73 1.94 — 2.1 —

Materials and Methods Starting Materials

All starting materials for synthesis were purchased commercially andwere used without further purification. Lead(II) acetate trihydratepuriss. p.a., ACS, 99.5-102.0%, Tin(II) chloride dihydrate puriss. p.a.,ACS, ≥98%, Methylamine hydrochloride ≥98%, Formamidine acetate 99%,Hypophosphorous acid solution 50 wt. % in H₂O, Hydriodic acid 57 wt. %in H₂O, distilled, stabilized, 99.95%, Ethylenediamine ReagentPlus®,≥99% and Dimethyl sulfoxide-d₆ 99.9 atom % D were purchased fromAldrich. 20 mL glass scintillation vials were used in all the synthesesof the materials. The same batch of starting materials was used in allsyntheses.

¹H-NMR Measurements

¹H NMR spectra were recorded on 600 MHz Bruker, A600 spectrometer. Allsamples were prepared by dissolving a small portion of the dried solids(˜10 mg) in a DMSO-d₆ solution (0.5 mL). The actual amount of en (x)that residing in the crystal structure was determined by ¹H-NMRspectroscopy. The (x) value was used for the calculations of all theexamined crystal formulas.

From NMR spectroscopy, it was possible to calculate only the ratiobetween en and MA, FA molecules. In order to find a way to quantify theamount of en relative to the MA, another equation was introduced thatincluded the two molecules, namely:

en+MA=1  (eq. 1)

This means that since there were only two organic molecules in thestructure, the total organic content should have been equal to 1 (or100%). Therefore, the actual amount of en (x) is the solution of thesystem of the two equations, equation (1), and the ratio found from theNMR spectra. This is the amount of en that was used in all formulacalculations and is mentioned in Table 13 and Tables 14-16.

XRD Measurements Single-Crystal X-Ray Diffraction

Single crystal diffraction experiments were performed using either aSTOE IPDS II or IPDS 2T diffractometer using Mo Kα radiation (λ=0.71073Å) and operating at 50 kV and 40 mA. Integration and numericalabsorption corrections were performed using the X-AREA, X-RED, andX-SHAPE programs. The structure was solved by charge flipping andrefined by full-matrix least squares on F² with the Jana2006 package.(See, e.g., Petricek, V., et al., 2014, 229, 345.)

Powder X-Ray Diffraction

Powder X-ray diffraction patterns were collected on a Rigaku Miniflexsystem (CuKα radiation) operated at 40 kV and 15 mA. A typical scan ratewas 10 sec/step with a step size of 0.02 deg. The data were manipulatedwith CMPR, and Rietveld analysis was performed with the Jana2006package. (See, e.g., Toby, B., J. Appl. Crystallogr. 2005, 38, 1040.)All PXRD patterns were recorded on the same in-house instrument, exceptfor the patterns used in PDF analysis, where they were recorded atsynchrotron.

Pair Distribution Function Analysis

For the synchrotron total scattering measurements, samples of finepowder, obtained by the means described above, were transferred intoKapton capillaries (0.81 mm OD, 0.8 mm ID) and tightly compacted toensure a maximum packing fraction. Both ends of the capillaries weresealed with epoxy and stored at RT. The synchrotron X-ray totalscattering measurements were recorded on the 11-ID-B beam line at theAdvanced Photon Source located at Argonne National Laboratory.

Optical Spectroscopy

Optical diffuse-reflectance measurements were performed at roomtemperature using a Shimadzu UV-3600 PC double-beam,double-monochromator spectrophotometer operating from 200 to 2500 nm.BaSO₄ was used as a non-absorbing reflectance reference. The generatedreflectance-versus-wavelength data were used to estimate the band gap ofthe material by converting reflectance to absorbance data according tothe Kubelka-Munk equation: α/S=(1−R)2/2R, where R is the reflectance andα and S are the absorption and scattering coefficients, respectively.(See, e.g., Gate, L. F., Appl. Opt. 1974, 13, 236.)

PL Measurements

All samples were measured using a Horiba LabRam Evolutionhigh-resolution confocal Raman microscope spectrometer (600 g/mmdiffraction grating) equipped with a diode continuous wave laser (473nm, 25 mW) and a Synapse charge-coupled device camera. The maximum poweroutput of the laser source was filtered to 1% of the maximum poweroutput.

TGA Measurements

The Thermogravimetric Analysis (TGA) measurements were performed on aNetzsch's Simultaneous Thermal Analysis (STA) system. An amount of ˜15mg of sample was placed inside an alumina cap and heated up to 700° C.under He flow with a heating rate of 8° C./min.

SEM/EDX

Scanning Electron Microscopy (SEM) measurements were recorded on ahigh-resolution field emission Hitachi SU8030. A Hitachi S3400N-IIinstrument equipped with a PGT energy-dispersive X-ray analyser was usedfor the EDX measurements. Data were acquired with an acceleratingvoltage of 20 kV.

Density Measurements

A Micromeritics AccuPyc II 1340 pycnometer was utilized for the densitydetermination of all samples. An amount of 400 mg of dry sample wasloaded into an aluminum cap (1 mL) and the volume determination wasperformed based on He displacement. Each sample was measured 5 times,and the sample volume was recorded along with the standard deviation.The average volume of each sample was used for the density calculations.

DFT Calculations

First-principles electronic structure calculations were carried outwithin the density functional theory (DFT) formalism using the ProjectorAugmented Wave method implemented in Vienna Ab-initio SimulationPackage. (See, e.g., Blöchl, P. E., Phys. Rev. B 1994, 50, 17953; andKresse, G., et al., Phys. Rev. B 1996, 54, 11169.) The internal atomicpositions were optimized until the atomic forces on each atom were lessthan 0.01 eV/Å with the plane-wave cutoff energy of 350 eV and a 4×3×3Γ-centered Monkhorst-Pack k-point grid, while the volume and shape ofthe unit cell were fixed. Multiple possible orientations of PbI₂vacancies in the single-vacancy supercells and multiple configurationsof PbI₂ vacancies in two-vacancy supercells were considered, andlowest-energy configurations were selected for further band structureanalysis. For the exchange-correlation function, the generalizedgradient approximation (GGA) was employed within Perdew-Burke-Ernzerhof(PBE) formalism and the spin-orbit coupling (SOC) was included in thecalculation. (See, e.g., Perdew, J. P., et al., Phys. Rev. Lett. 1996,77, 3865.)

Syntheses Syntheses of (MA)_(1−x/2)(en)_(x/2)(Sn)_(1−x/2)(I)_(3−x/2) (x:0%, 5%, 9%, 21%, 24%, 36%, 40%)

α-MASnI₃: 679.95 mg (3 mmol) of SnCl₂.2H₂O were dissolved in a solutionconsisting of 8 mL of 57% w/w aqueous HI and 1.5 mL of 50% aqueousH₃PO₂, by heating to boiling under constant magnetic stirring. Then202.56 mg (3 mmol) of methylamine hydrochloride were added to the hotyellow solution, leading to the formation of black crystals. Thecrystals were collected by suction filtration and dried in a vacuum ovenat 110° C. for 12 h. Yield: 637 mg, (40% based on Sn).

x=5%: 679.95 mg (3 mmol) of SnCl₂.2H₂O were dissolved in a 57% w/waqueous HI solution (8 mL) by heating to boiling under constant magneticstirring for about 5 minutes. Then 20 μL of ethylenediamine (0.3 mmol)were added to 50% aqueous H₃PO₂ (1.5 mL) at RT. This solution was addedto the hot reaction solution. Subsequent addition of 202.56 mg (3 mmol)of methylamine hydrochloride to the hot yellow solution lead to theformation of black crystals. Stirring was continued for 5 min. Thecrystals were collected by suction filtration and dried in a vacuum ovenat 110° C. for 12 h. Yield: 630 mg, (39.5% based on Sn).

x=9%: 679.95 mg (3 mmol) of SnCl₂.2H₂O were dissolved in a 57% w/waqueous HI solution (8 mL) by heating to boiling under constant magneticstirring for about 5 minutes. Then 40 μL of ethylenediamine (0.6 mmol)were added to 50% aqueous H₃PO₂ (1.5 mL) at RT. This solution was addedto the hot reaction solution. Subsequent addition of 202.56 mg (3 mmol)of methylamine hydrochloride to the hot yellow solution led to theformation of black crystals. Stirring was continued for 5 min. Thecrystals were collected by suction filtration and dried in a vacuum ovenat 110° C. for 12 h. Yield: 640 mg, (40.1% based on Sn).

x=21%: 679.95 mg (3 mmol) of SnCl₂.2H₂O were dissolved in a 57% w/waqueous HI solution (8 mL) by heating to boiling under constant magneticstirring for about 5 minutes. Then 100 μL of ethylenediamine (1.5 mmol)were added to 50% aqueous H₃PO₂ (1.5 mL) at RT. This solution was addedto the hot reaction solution. Subsequent addition of 202.56 mg (3 mmol)of methylamine hydrochloride to the hot yellow solution led to theformation of black crystals. Stirring was continued for 5 min. Thecrystals were collected by suction filtration and dried in a vacuum ovenat 110° C. for 12 h. Yield: 646 mg, (40.5% based on Sn).

x=24%: 679.95 mg (3 mmol) of SnCl₂.2H₂O were dissolved in a 57% w/waqueous HI solution (8 mL) by heating to boiling under constant magneticstirring for about 5 minutes. Then 120 μL of ethylenediamine (1.8 mmol)were added to 50% aqueous H₃PO₂ (1.5 mL) at RT. This solution was addedto the hot reaction solution. Subsequent addition of 202.56 mg (3 mmol)of methylamine hydrochloride to the hot yellow solution led to theformation of black crystals. Stirring was continued for 5 min. Thecrystals were collected by suction filtration and dried in a vacuum ovenat 110° C. for 12 h. Yield: 635 mg, (39.8% based on Sn).

x=36%: 679.95 mg (3 mmol) of SnCl₂.2H₂O were dissolved in a 57% w/waqueous HI solution (8 mL) by heating to boiling under constant magneticstirring for about 5 minutes. Then 160 μL of ethylenediamine (2.4 mmol)were added to 50% aqueous H₃PO₂ (1.5 mL) at RT. This solution was addedto the hot reaction solution. Subsequent addition of 202.56 mg (3 mmol)of methylamine hydrochloride to the hot yellow solution led to theformation of black crystals. Stirring was continued for 5 min. Thecrystals were collected by suction filtration and dried in a vacuum ovenat 110° C. for 12 h. Yield: 620 mg, (38.9% based on Sn).

x=40%: 679.95 mg (3 mmol) of SnCl₂.2H₂O were dissolved in a 57% w/waqueous HI solution (8 mL) by heating to boiling under constant magneticstirring for about 5 minutes. Then 200 μL of ethylenediamine (3 mmol)were added to 50% aqueous H₃PO₂ (1.5 mL) at RT. This solution was addedto the hot reaction solution. Subsequent addition of 202.56 mg (3 mmol)of methylamine hydrochloride to the hot yellow solution led to theformation of black crystals. Stirring was continued for 5 min. Thecrystals were collected by suction filtration and dried in a vacuum ovenat 110° C. for 12 h. Yield: Yield: 610 mg, (38.3% based on Sn).

Syntheses of (FA)_(1−x/2)(en)_(x/2)(Pb)_(1−x/2)(I)_(3−x/2) (x: 0%, 7%,11%, 21%, 27%, 29%, 39%)

α-FAPbI₃: 1137 mg (3 mmol) of Pb(CH₃CO₂)₂.3H₂O were dissolved in asolution consisting of 8 mL of 57% w/w aqueous HI and 1.2 mL of 50%aqueous H₃PO₂, by heating to boiling under constant magnetic stirring.Then 312 mg (3 mmol) of formamidine acetate were added to the hot yellowsolution, leading to the formation of yellow crystals (δ phase). Thereaction mixture was heated for additional 10 min, where all the yellowcrystals turned black (αphase). The crystals were collected immediatelyby suction filtration and dried in a vacuum oven at 110° C. for 12 h.Yield: 1044 mg, (55% based on Pb).

x=7%: 1137 mg (3 mmol) of Pb(CH₃CO₂)₂.3H₂O were dissolved in a 57% w/waqueous HI solution (8 mL) by heating to boiling under constant magneticstirring for about 5 minutes. Then 20 μL of ethylenediamine (0.3 mmol)were added to 50% aqueous H₃PO₂ (1.2 mL) at RT. This solution was addedto the hot reaction solution. Subsequent addition of 312 mg (3 mmol) offormamidine acetate to the hot yellow solution led to the formation ofblack crystals. Stirring was continued for 5 min. The crystals werecollected by suction filtration and dried in a vacuum oven at 110° C.for 12 h. Yield: 1065 mg, (56% based on Pb).

x=11%: 1137 mg (3 mmol) of Pb(CH₃CO₂)₂.3H₂O were dissolved in a 57% w/waqueous HI solution (8 mL) by heating to boiling under constant magneticstirring for about 5 minutes. Then 40 μL of ethylenediamine (0.6 mmol)were added to 50% aqueous H₃PO₂ (1.2 mL) at RT. This solution was addedto the hot reaction solution. Subsequent addition of 312 mg (3 mmol) offormamidine acetate to the hot yellow solution led to the formation ofblack crystals. Stirring was continued for 5 min. The crystals werecollected by suction filtration and dried in a vacuum oven at 110° C.for 12 h. Yield: 1101 mg, (58% based on Pb).

x=21%: 1137 mg (3 mmol) of Pb(CH₃CO₂)₂.3H₂O were dissolved in a 57% w/waqueous HI solution (8 mL) by heating to boiling under constant magneticstirring for about 5 minutes. Then 100 μL of ethylenediamine (1.5 mmol)were added to 50% aqueous H₃PO₂ (1.2 mL) at RT. This solution was addedto the hot reaction solution. Subsequent addition of 312 mg (3 mmol) offormamidine acetate to the hot yellow solution led to the formation ofblack crystals. Stirring was continued for 5 min. The crystals werecollected by suction filtration and dried in a vacuum oven at 110° C.for 12 h. Yield: 1006 mg, (53% based on Pb).

x=27%: 1137 mg (3 mmol) of Pb(CH₃CO₂)₂.3H₂O were dissolved in a 57% w/waqueous HI solution (8 mL) by heating to boiling under constant magneticstirring for about 5 minutes. Then 140 μL of ethylenediamine (2.1 mmol)were added to 50% aqueous H₃PO₂ (1.2 mL) at RT. This solution was addedto the hot reaction solution. Subsequent addition of 312 mg (3 mmol) offormamidine acetate to the hot yellow solution led to the formation ofblack crystals. Stirring was continued for 5 min. The crystals werecollected by suction filtration and dried in a vacuum oven at 110° C.for 12 h. Yield: 968 mg, (51% based on Pb).

x=29%: 1137 mg (3 mmol) of Pb(CH₃CO₂)₂/3H₂O were dissolved in a 57% w/waqueous HI solution (8 mL) by heating to boiling under constant magneticstirring for about 5 minutes. Then 160 μL of ethylenediamine (2.4 mmol)were added to 50% aqueous H₃PO₂ (1.2 mL) at RT. This solution was addedto the hot reaction solution. Subsequent addition of 312 mg (3 mmol) offormamidine acetate to the hot yellow solution led to the formation ofblack crystals. Stirring was continued for 5 min. The crystals werecollected by suction filtration and dried in a vacuum oven at 110° C.for 12 h. Yield: 930 mg, (49% based on Pb).

x=39%: 1137 mg (3 mmol) of Pb(CH₃CO₂)₂.3H₂O were dissolved in a 57% w/waqueous HI solution (10 mL) by heating to boiling under constantmagnetic stirring for about 5 minutes. Then 200 μL of ethylenediamine (3mmol) were added to 50% aqueous H₃PO₂ (1.2 mL) at RT. This solution wasadded to the hot reaction solution. Following this, 312 mg (3 mmol) offormamidine acetate were added to the hot yellow solution, giving riseto the precipitation of a black powder, which was rapidly dissolvedunder stirring to afford a clear bright yellow solution. The stirringwas then discontinued, and the solution was left to cool to roomtemperature. Upon cooling, dark red crystals were deposited. Thecrystals were collected by suction filtration and dried in a vacuum ovenat 110° C. for 12 h. Yield: 720 mg, (38% based on Pb).

Syntheses of (MA)_(1−x/2)(en)_(x/2)(Pb)_(1−x/2)(I)_(3−x/2) (x: 0%, 3%,10%, 29%, 35%, 40%, 44%)

β-MAPbI₃: 1137 mg (3 mmol) of Pb(CH₃CO₂)₂.3H₂O were dissolved in asolution consisting of 5 mL of 57% w/w aqueous HI and 1.2 mL of 50%aqueous H₃PO₂, by heating to boiling under constant magnetic stirring.Then 202.56 mg (3 mmol) of methylamine hydrochloride were added to thehot yellow solution, leading to the formation of black crystals. Thecrystals were collected by suction filtration and dried in a vacuum ovenat 110° C. for 12 h. Yield: 837 mg, (45% based on Pb).

x=3%: 1137 mg (3 mmol) of Pb(CH₃CO₂)₂.3H₂O were dissolved in a 57% w/waqueous HI solution (5 mL) by heating to boiling under constant magneticstirring for about 5 minutes. Then 20 μL of ethylenediamine (0.3 mmol)were added to 50% aqueous H₃PO₂ (1.2 mL) at RT. This solution was addedto the hot reaction solution. Subsequent addition of 202.56 mg (3 mmol)of methylamine hydrochloride to the hot yellow solution led to theformation of black crystals. The crystals were collected by suctionfiltration and dried in a vacuum oven at 110° C. for 12 h. Yield: 818mg, (44% based on Pb).

x=10%: 1137 mg (3 mmol) of Pb(CH₃CO₂)₂.3H₂O were dissolved in a 57% w/waqueous HI solution (5 mL) by heating to boiling under constant magneticstirring for about 5 minutes. Then 40 μL of ethylenediamine (0.6 mmol)were added to 50% aqueous H₃PO₂ (1.2 mL) at RT. This solution was addedto the hot reaction solution. Subsequent addition of 202.56 mg (3 mmol)of methylamine hydrochloride to the hot yellow solution led to theformation of black crystals. The crystals were collected by suctionfiltration and dried in a vacuum oven at 110° C. for 12 h. Yield: 874mg, (47% based on Pb).

x=29%: 1137 mg (3 mmol) of Pb(CH₃CO₂)₂.3H₂O were dissolved in a 57% w/waqueous HI solution (5 mL) by heating to boiling under constant magneticstirring for about 5 minutes. Then 100 μL of ethylenediamine (1.5 mmol)were added to 50% aqueous H₃PO₂ (1.2 mL) at RT. This solution was addedto the hot reaction solution. Subsequent addition of 202.56 mg (3 mmol)of methylamine hydrochloride to the hot yellow solution led to theformation of black crystals. The crystals were collected by suctionfiltration and dried in a vacuum oven at 110° C. for 12 h. Yield: 781mg, (42% based on Pb).

x=35%: 1137 mg (3 mmol) of Pb(CH₃CO₂)₂.3H₂O were dissolved in a 57% w/waqueous HI solution (5 mL) by heating to boiling under constant magneticstirring for about 5 minutes. Then 120 μL of ethylenediamine (1.8 mmol)were added to 50% aqueous H₃PO₂ (1.2 mL) at RT. This solution was addedto the hot reaction solution. Following this, 202.56 mg (3 mmol) ofmethylamine hydrochloride were added to the hot yellow solution. Thestirring was then discontinued, and the solution was left to cool toroom temperature. Upon cooling, dark red crystals were deposited. Thecrystals were collected by suction filtration and dried in a vacuum ovenat 110° C. for 12 h. Yield: 725 mg, (39% based on Pb).

x=40%: 1137 mg (3 mmol) of Pb(CH₃CO₂)₂.3H₂O were dissolved in a 57% w/waqueous HI solution (5 mL) by heating to boiling under constant magneticstirring for about 5 minutes. Then 140 μL of ethylenediamine (2.1 mmol)were added to 50% aqueous H₃PO₂ (1.2 mL) at RT. This solution was addedto the hot reaction solution. Following this, 202.56 mg (3 mmol) ofmethylamine hydrochloride were added to the hot yellow solution. Thestirring was then discontinued, and the solution was left to cool toroom temperature. Upon cooling, red crystals were deposited. Thecrystals were collected by suction filtration and dried in a vacuum ovenat 110° C. for 12 h. Yield: 632 mg, (34% based on Pb).

x=44%: 1137 mg (3 mmol) of Pb(CH₃CO₂)₂.3H₂O were dissolved in a 57% w/waqueous HI solution (5 mL) by heating to boiling under constant magneticstirring for about 5 minutes. Then 200 μL of ethylenediamine (3 mmol)were added to 50% aqueous H₃PO₂ (1 mL) at RT. This solution was added tothe hot reaction solution. Following this, 202.56 mg (3 mmol) ofmethylamine hydrochloride were added to the hot yellow solution. Thestirring was then discontinued, and the solution was left to cool toroom temperature. Upon cooling, orange crystals were deposited. Thecrystals were collected by suction filtration and dried in a vacuum ovenat 110° C. for 12 h. Yield: 465 mg, (25% based on Pb).

Example 4

Diammonium cations were added to the synthesis of CsSnI₃ (CsSnI₃+10%enI₂) using the techniques described herein to form crystals of the 3Dperovskite en/CsSnI₃. The J-V curves for: (1) a solar cell using theen/CsSnI₃ as an absorber; and (2) a solar cell using CsSnI₃ as anabsorber under a reverse voltage scan are shown in FIG. 26A. Thenormalized PCE for the two solar cells as a function of time is shown inFIG. 26B. These aging tests were conducting under constant AM1.5Gillumination in ambient air.

The word “illustrative” is used herein to mean serving as an example,instance, or illustration. Any aspect or design described herein as“illustrative” is not necessarily to be construed as preferred oradvantageous over other aspects or designs. Further, for the purposes ofthis disclosure and unless otherwise specified, “a” or “an” means “oneor more.”

The foregoing description of illustrative embodiments of the inventionhas been presented for purposes of illustration and of description. Itis not intended to be exhaustive or to limit the invention to theprecise form disclosed, and modifications and variations are possible inlight of the above teachings or may be acquired from practice of theinvention. The embodiments were chosen and described in order to explainthe principles of the invention and as practical applications of theinvention to enable one skilled in the art to utilize the invention invarious embodiments and with various modifications as suited to theparticular use contemplated. It is intended that the scope of theinvention be defined by the claims appended hereto and theirequivalents.

1. Discrete single-crystals of a halide perovskite having athree-dimensional amAMX₃ perovskite crystal structure, wherein am is analkyl diamine cation, an aromatic diamine cation, an aromatic azolecation, a cyclic alkyl diamine cation or a hydrazinediium cation; A is amonovalent alkylammonium cation or an alkali metal cation, X is a halideion, and M is an octahedrally coordinated bivalent metal atom.
 2. Thesingle-crystals of claim 1, wherein A comprises a monovalentalkylammonium cation.
 3. The single-crystals of claim 2, wherein A ismethylammonium.
 4. The single-crystals of claim 2, wherein A isformamidinium.
 5. The single-crystals of claim 4, wherein M is tin. 6.The single-crystals of claim 5, wherein am comprises ethylenediammonium.
 7. The single-crystals of claim 2, wherein M is tin.
 8. Thesingle-crystals of claim 1, wherein am comprises ethylene diammonium. 9.The single-crystals of claim 8, wherein A comprises a monovalentalkylammonium cation.
 10. The single-crystals of claim 9, wherein Mcomprises tin or lead.
 11. The single-crystals of claim 1, whereinhalide perovskite having a three-dimensional enMASnI₃ perovskite crystalstructure.
 12. The single-crystals of claim 1, wherein halide perovskitehaving a three-dimensional enFASnI₃ perovskite crystal structure. 13.The single-crystals of claim 1, wherein halide perovskite having athree-dimensional enFAPbI₃ perovskite crystal structure.
 14. Thesingle-crystals of claim 1, wherein A is an alkali metal cation.
 15. Thesingle-crystals of claim 14, wherein the alkali metal cation is a cesiumcation.
 16. The single-crystals of claim 14, wherein halide perovskitehas a three-dimensional enCsSnI₃ perovskite crystal structure.
 17. Thesingle-crystals of claim 1, having a molar ratio of A to am in the rangefrom 1:0.05 to 1:1.
 18. An electronic device comprising: (a) a firstelectrically conductive contact; (b) a second electrically conductivecontact; and (c) a photoactive material in electrical communication withthe first and second electrically conductive contacts, the photoactivematerial comprising discrete single-crystals of a halide perovskitehaving a three-dimensional amAMX₃ perovskite crystal structure, whereinam is an alkyl diamine cation, an aromatic diamine cation, an aromaticazole cation, a cyclic alkyl diamine cation or a hydrazinediium cation,A is a monovalent alkylammonium cation or an alkali metal cation, X is ahalide ion, and M is an octahedrally coordinated bivalent metal atom,wherein the first and second electrically conductive contacts areconfigured to apply and electric field across the photoactive materialand/or to pass an electric current through the photoactive material. 19.A photovoltaic cell comprising: (a) a first electrode comprising anelectrically conductive material; (b) a second electrode comprising anelectrically conductive material; (c) a photoactive material disposedbetween, and in electrical communication with, the first and secondelectrodes, the photoactive material comprising discrete single-crystalsof a halide perovskite having a three-dimensional amAMX₃ perovskitecrystal structure, wherein am is an alkyl diamine cation, an aromaticdiamine cation, an aromatic azole cation, a cyclic alkyl diamine cationor a hydrazinediium cation; A is a monovalent alkylammonium cation or analkali metal cation, X is a halide ion, and M is an octahedrallycoordinated bivalent metal atom; and (d) a hole transporting materialdisposed between the first and second electrodes and configured tofacilitate the transport of holes generated in the photoactive materialto one of the first and second electrodes.
 20. A crystalline halideperovskite having a three-dimensional amAMX₃ perovskite crystalstructure, wherein am is an alkyl diamine cation, an aromatic diaminecation, an aromatic azole cation, a cyclic alkyl diamine cation or ahydrazinediium cation; A is an alkali metal cation, X is a halide ion,and M is an octahedrally coordinated bivalent metal atom.
 21. The halideperovskite of claim 20 having a three-dimensional enCsSnI₃ perovskitecrystal structure.
 22. A crystalline halide perovskite having athree-dimensional amAMX₃ perovskite crystal structure, selected fromamMASnI₃, enFASnI₃, and enFAPbI₃, wherein am is an alkyl diamine cation,an aromatic diamine cation, an aromatic azole cation, a cyclic alkyldiamine cation or a hydrazinediium cation; A is an alkali metal cation,X is a halide ion, and M is an octahedrally coordinated bivalent metalatom.
 23. The halide perovskite of claim 22, wherein am is ethylenediammonium.